Properties

Label 9600.2.a
Level $9600$
Weight $2$
Character orbit 9600.a
Rep. character $\chi_{9600}(1,\cdot)$
Character field $\Q$
Dimension $152$
Newform subspaces $100$
Sturm bound $3840$
Trace bound $17$

Related objects

Downloads

Learn more

Defining parameters

Level: \( N \) \(=\) \( 9600 = 2^{7} \cdot 3 \cdot 5^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 9600.a (trivial)
Character field: \(\Q\)
Newform subspaces: \( 100 \)
Sturm bound: \(3840\)
Trace bound: \(17\)
Distinguishing \(T_p\): \(7\), \(11\), \(13\), \(17\), \(29\), \(31\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_0(9600))\).

Total New Old
Modular forms 2016 152 1864
Cusp forms 1825 152 1673
Eisenstein series 191 0 191

The following table gives the dimensions of the cuspidal new subspaces with specified eigenvalues for the Atkin-Lehner operators and the Fricke involution.

\(2\)\(3\)\(5\)FrickeDim.
\(+\)\(+\)\(+\)\(+\)\(17\)
\(+\)\(+\)\(-\)\(-\)\(22\)
\(+\)\(-\)\(+\)\(-\)\(19\)
\(+\)\(-\)\(-\)\(+\)\(18\)
\(-\)\(+\)\(+\)\(-\)\(19\)
\(-\)\(+\)\(-\)\(+\)\(18\)
\(-\)\(-\)\(+\)\(+\)\(17\)
\(-\)\(-\)\(-\)\(-\)\(22\)
Plus space\(+\)\(70\)
Minus space\(-\)\(82\)

Trace form

\( 152 q + 152 q^{9} + O(q^{10}) \) \( 152 q + 152 q^{9} - 16 q^{17} - 16 q^{41} + 120 q^{49} - 32 q^{57} + 16 q^{73} + 152 q^{81} + 48 q^{89} - 80 q^{97} + O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(9600))\) into newform subspaces

Label Char Prim Dim $A$ Field CM Traces A-L signs Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$ 2 3 5
9600.2.a.a 9600.a 1.a $1$ $76.656$ \(\Q\) None \(0\) \(-1\) \(0\) \(-4\) $+$ $+$ $+$ $\mathrm{SU}(2)$ \(q-q^{3}-4q^{7}+q^{9}-6q^{11}+4q^{13}+\cdots\)
9600.2.a.b 9600.a 1.a $1$ $76.656$ \(\Q\) None \(0\) \(-1\) \(0\) \(-4\) $-$ $+$ $+$ $\mathrm{SU}(2)$ \(q-q^{3}-4q^{7}+q^{9}-2q^{11}+4q^{21}+\cdots\)
9600.2.a.c 9600.a 1.a $1$ $76.656$ \(\Q\) None \(0\) \(-1\) \(0\) \(-4\) $+$ $+$ $-$ $\mathrm{SU}(2)$ \(q-q^{3}-4q^{7}+q^{9}-6q^{13}-2q^{17}+\cdots\)
9600.2.a.d 9600.a 1.a $1$ $76.656$ \(\Q\) None \(0\) \(-1\) \(0\) \(-4\) $+$ $+$ $-$ $\mathrm{SU}(2)$ \(q-q^{3}-4q^{7}+q^{9}+6q^{13}+2q^{17}+\cdots\)
9600.2.a.e 9600.a 1.a $1$ $76.656$ \(\Q\) None \(0\) \(-1\) \(0\) \(-2\) $-$ $+$ $+$ $\mathrm{SU}(2)$ \(q-q^{3}-2q^{7}+q^{9}-4q^{11}+2q^{13}+\cdots\)
9600.2.a.f 9600.a 1.a $1$ $76.656$ \(\Q\) None \(0\) \(-1\) \(0\) \(-2\) $-$ $+$ $+$ $\mathrm{SU}(2)$ \(q-q^{3}-2q^{7}+q^{9}-2q^{11}-6q^{13}+\cdots\)
9600.2.a.g 9600.a 1.a $1$ $76.656$ \(\Q\) None \(0\) \(-1\) \(0\) \(-2\) $+$ $+$ $+$ $\mathrm{SU}(2)$ \(q-q^{3}-2q^{7}+q^{9}+2q^{11}-2q^{13}+\cdots\)
9600.2.a.h 9600.a 1.a $1$ $76.656$ \(\Q\) None \(0\) \(-1\) \(0\) \(-2\) $-$ $+$ $+$ $\mathrm{SU}(2)$ \(q-q^{3}-2q^{7}+q^{9}+4q^{11}+6q^{13}+\cdots\)
9600.2.a.i 9600.a 1.a $1$ $76.656$ \(\Q\) None \(0\) \(-1\) \(0\) \(-2\) $-$ $+$ $+$ $\mathrm{SU}(2)$ \(q-q^{3}-2q^{7}+q^{9}+6q^{11}+2q^{13}+\cdots\)
9600.2.a.j 9600.a 1.a $1$ $76.656$ \(\Q\) None \(0\) \(-1\) \(0\) \(0\) $-$ $+$ $-$ $\mathrm{SU}(2)$ \(q-q^{3}+q^{9}-4q^{11}-2q^{13}+2q^{17}+\cdots\)
9600.2.a.k 9600.a 1.a $1$ $76.656$ \(\Q\) None \(0\) \(-1\) \(0\) \(0\) $-$ $+$ $-$ $\mathrm{SU}(2)$ \(q-q^{3}+q^{9}-4q^{11}+2q^{13}+2q^{17}+\cdots\)
9600.2.a.l 9600.a 1.a $1$ $76.656$ \(\Q\) None \(0\) \(-1\) \(0\) \(0\) $+$ $+$ $+$ $\mathrm{SU}(2)$ \(q-q^{3}+q^{9}-2q^{11}-4q^{13}-q^{27}+\cdots\)
9600.2.a.m 9600.a 1.a $1$ $76.656$ \(\Q\) None \(0\) \(-1\) \(0\) \(0\) $+$ $+$ $-$ $\mathrm{SU}(2)$ \(q-q^{3}+q^{9}-2q^{11}-2q^{13}-2q^{17}+\cdots\)
9600.2.a.n 9600.a 1.a $1$ $76.656$ \(\Q\) None \(0\) \(-1\) \(0\) \(0\) $-$ $+$ $-$ $\mathrm{SU}(2)$ \(q-q^{3}+q^{9}-2q^{11}+2q^{13}-2q^{17}+\cdots\)
9600.2.a.o 9600.a 1.a $1$ $76.656$ \(\Q\) None \(0\) \(-1\) \(0\) \(0\) $+$ $+$ $+$ $\mathrm{SU}(2)$ \(q-q^{3}+q^{9}-2q^{11}+4q^{13}-q^{27}+\cdots\)
9600.2.a.p 9600.a 1.a $1$ $76.656$ \(\Q\) None \(0\) \(-1\) \(0\) \(0\) $-$ $+$ $-$ $\mathrm{SU}(2)$ \(q-q^{3}+q^{9}+2q^{11}-2q^{13}+2q^{17}+\cdots\)
9600.2.a.q 9600.a 1.a $1$ $76.656$ \(\Q\) None \(0\) \(-1\) \(0\) \(0\) $-$ $+$ $-$ $\mathrm{SU}(2)$ \(q-q^{3}+q^{9}+2q^{11}+2q^{13}+2q^{17}+\cdots\)
9600.2.a.r 9600.a 1.a $1$ $76.656$ \(\Q\) None \(0\) \(-1\) \(0\) \(0\) $+$ $+$ $-$ $\mathrm{SU}(2)$ \(q-q^{3}+q^{9}+4q^{11}-2q^{13}-2q^{17}+\cdots\)
9600.2.a.s 9600.a 1.a $1$ $76.656$ \(\Q\) None \(0\) \(-1\) \(0\) \(0\) $-$ $+$ $-$ $\mathrm{SU}(2)$ \(q-q^{3}+q^{9}+4q^{11}+2q^{13}-2q^{17}+\cdots\)
9600.2.a.t 9600.a 1.a $1$ $76.656$ \(\Q\) None \(0\) \(-1\) \(0\) \(2\) $+$ $+$ $+$ $\mathrm{SU}(2)$ \(q-q^{3}+2q^{7}+q^{9}-4q^{11}-2q^{13}+\cdots\)
9600.2.a.u 9600.a 1.a $1$ $76.656$ \(\Q\) None \(0\) \(-1\) \(0\) \(2\) $-$ $+$ $+$ $\mathrm{SU}(2)$ \(q-q^{3}+2q^{7}+q^{9}-2q^{11}+6q^{13}+\cdots\)
9600.2.a.v 9600.a 1.a $1$ $76.656$ \(\Q\) None \(0\) \(-1\) \(0\) \(2\) $+$ $+$ $+$ $\mathrm{SU}(2)$ \(q-q^{3}+2q^{7}+q^{9}+2q^{11}+2q^{13}+\cdots\)
9600.2.a.w 9600.a 1.a $1$ $76.656$ \(\Q\) None \(0\) \(-1\) \(0\) \(2\) $-$ $+$ $+$ $\mathrm{SU}(2)$ \(q-q^{3}+2q^{7}+q^{9}+4q^{11}-6q^{13}+\cdots\)
9600.2.a.x 9600.a 1.a $1$ $76.656$ \(\Q\) None \(0\) \(-1\) \(0\) \(2\) $+$ $+$ $+$ $\mathrm{SU}(2)$ \(q-q^{3}+2q^{7}+q^{9}+6q^{11}-2q^{13}+\cdots\)
9600.2.a.y 9600.a 1.a $1$ $76.656$ \(\Q\) None \(0\) \(-1\) \(0\) \(4\) $-$ $+$ $+$ $\mathrm{SU}(2)$ \(q-q^{3}+4q^{7}+q^{9}-6q^{11}-4q^{13}+\cdots\)
9600.2.a.z 9600.a 1.a $1$ $76.656$ \(\Q\) None \(0\) \(-1\) \(0\) \(4\) $-$ $+$ $+$ $\mathrm{SU}(2)$ \(q-q^{3}+4q^{7}+q^{9}-2q^{11}-4q^{21}+\cdots\)
9600.2.a.ba 9600.a 1.a $1$ $76.656$ \(\Q\) None \(0\) \(-1\) \(0\) \(4\) $-$ $+$ $-$ $\mathrm{SU}(2)$ \(q-q^{3}+4q^{7}+q^{9}-6q^{13}+2q^{17}+\cdots\)
9600.2.a.bb 9600.a 1.a $1$ $76.656$ \(\Q\) None \(0\) \(-1\) \(0\) \(4\) $+$ $+$ $-$ $\mathrm{SU}(2)$ \(q-q^{3}+4q^{7}+q^{9}+6q^{13}-2q^{17}+\cdots\)
9600.2.a.bc 9600.a 1.a $1$ $76.656$ \(\Q\) None \(0\) \(1\) \(0\) \(-4\) $-$ $-$ $-$ $\mathrm{SU}(2)$ \(q+q^{3}-4q^{7}+q^{9}-6q^{13}+2q^{17}+\cdots\)
9600.2.a.bd 9600.a 1.a $1$ $76.656$ \(\Q\) None \(0\) \(1\) \(0\) \(-4\) $+$ $-$ $-$ $\mathrm{SU}(2)$ \(q+q^{3}-4q^{7}+q^{9}+6q^{13}-2q^{17}+\cdots\)
9600.2.a.be 9600.a 1.a $1$ $76.656$ \(\Q\) None \(0\) \(1\) \(0\) \(-4\) $-$ $-$ $+$ $\mathrm{SU}(2)$ \(q+q^{3}-4q^{7}+q^{9}+2q^{11}-4q^{21}+\cdots\)
9600.2.a.bf 9600.a 1.a $1$ $76.656$ \(\Q\) None \(0\) \(1\) \(0\) \(-4\) $+$ $-$ $+$ $\mathrm{SU}(2)$ \(q+q^{3}-4q^{7}+q^{9}+6q^{11}-4q^{13}+\cdots\)
9600.2.a.bg 9600.a 1.a $1$ $76.656$ \(\Q\) None \(0\) \(1\) \(0\) \(-2\) $+$ $-$ $+$ $\mathrm{SU}(2)$ \(q+q^{3}-2q^{7}+q^{9}-6q^{11}-2q^{13}+\cdots\)
9600.2.a.bh 9600.a 1.a $1$ $76.656$ \(\Q\) None \(0\) \(1\) \(0\) \(-2\) $+$ $-$ $+$ $\mathrm{SU}(2)$ \(q+q^{3}-2q^{7}+q^{9}-4q^{11}-6q^{13}+\cdots\)
9600.2.a.bi 9600.a 1.a $1$ $76.656$ \(\Q\) None \(0\) \(1\) \(0\) \(-2\) $-$ $-$ $+$ $\mathrm{SU}(2)$ \(q+q^{3}-2q^{7}+q^{9}-2q^{11}+2q^{13}+\cdots\)
9600.2.a.bj 9600.a 1.a $1$ $76.656$ \(\Q\) None \(0\) \(1\) \(0\) \(-2\) $+$ $-$ $+$ $\mathrm{SU}(2)$ \(q+q^{3}-2q^{7}+q^{9}+2q^{11}+6q^{13}+\cdots\)
9600.2.a.bk 9600.a 1.a $1$ $76.656$ \(\Q\) None \(0\) \(1\) \(0\) \(-2\) $+$ $-$ $+$ $\mathrm{SU}(2)$ \(q+q^{3}-2q^{7}+q^{9}+4q^{11}-2q^{13}+\cdots\)
9600.2.a.bl 9600.a 1.a $1$ $76.656$ \(\Q\) None \(0\) \(1\) \(0\) \(0\) $+$ $-$ $-$ $\mathrm{SU}(2)$ \(q+q^{3}+q^{9}-4q^{11}-2q^{13}-2q^{17}+\cdots\)
9600.2.a.bm 9600.a 1.a $1$ $76.656$ \(\Q\) None \(0\) \(1\) \(0\) \(0\) $+$ $-$ $-$ $\mathrm{SU}(2)$ \(q+q^{3}+q^{9}-4q^{11}+2q^{13}-2q^{17}+\cdots\)
9600.2.a.bn 9600.a 1.a $1$ $76.656$ \(\Q\) None \(0\) \(1\) \(0\) \(0\) $+$ $-$ $-$ $\mathrm{SU}(2)$ \(q+q^{3}+q^{9}-2q^{11}-2q^{13}+2q^{17}+\cdots\)
9600.2.a.bo 9600.a 1.a $1$ $76.656$ \(\Q\) None \(0\) \(1\) \(0\) \(0\) $-$ $-$ $-$ $\mathrm{SU}(2)$ \(q+q^{3}+q^{9}-2q^{11}+2q^{13}+2q^{17}+\cdots\)
9600.2.a.bp 9600.a 1.a $1$ $76.656$ \(\Q\) None \(0\) \(1\) \(0\) \(0\) $-$ $-$ $+$ $\mathrm{SU}(2)$ \(q+q^{3}+q^{9}+2q^{11}-4q^{13}+q^{27}+\cdots\)
9600.2.a.bq 9600.a 1.a $1$ $76.656$ \(\Q\) None \(0\) \(1\) \(0\) \(0\) $+$ $-$ $-$ $\mathrm{SU}(2)$ \(q+q^{3}+q^{9}+2q^{11}-2q^{13}-2q^{17}+\cdots\)
9600.2.a.br 9600.a 1.a $1$ $76.656$ \(\Q\) None \(0\) \(1\) \(0\) \(0\) $+$ $-$ $-$ $\mathrm{SU}(2)$ \(q+q^{3}+q^{9}+2q^{11}+2q^{13}-2q^{17}+\cdots\)
9600.2.a.bs 9600.a 1.a $1$ $76.656$ \(\Q\) None \(0\) \(1\) \(0\) \(0\) $+$ $-$ $+$ $\mathrm{SU}(2)$ \(q+q^{3}+q^{9}+2q^{11}+4q^{13}+q^{27}+\cdots\)
9600.2.a.bt 9600.a 1.a $1$ $76.656$ \(\Q\) None \(0\) \(1\) \(0\) \(0\) $+$ $-$ $-$ $\mathrm{SU}(2)$ \(q+q^{3}+q^{9}+4q^{11}-2q^{13}+2q^{17}+\cdots\)
9600.2.a.bu 9600.a 1.a $1$ $76.656$ \(\Q\) None \(0\) \(1\) \(0\) \(0\) $-$ $-$ $-$ $\mathrm{SU}(2)$ \(q+q^{3}+q^{9}+4q^{11}+2q^{13}+2q^{17}+\cdots\)
9600.2.a.bv 9600.a 1.a $1$ $76.656$ \(\Q\) None \(0\) \(1\) \(0\) \(2\) $+$ $-$ $+$ $\mathrm{SU}(2)$ \(q+q^{3}+2q^{7}+q^{9}-6q^{11}+2q^{13}+\cdots\)
9600.2.a.bw 9600.a 1.a $1$ $76.656$ \(\Q\) None \(0\) \(1\) \(0\) \(2\) $-$ $-$ $+$ $\mathrm{SU}(2)$ \(q+q^{3}+2q^{7}+q^{9}-4q^{11}+6q^{13}+\cdots\)
9600.2.a.bx 9600.a 1.a $1$ $76.656$ \(\Q\) None \(0\) \(1\) \(0\) \(2\) $+$ $-$ $+$ $\mathrm{SU}(2)$ \(q+q^{3}+2q^{7}+q^{9}-2q^{11}-2q^{13}+\cdots\)
9600.2.a.by 9600.a 1.a $1$ $76.656$ \(\Q\) None \(0\) \(1\) \(0\) \(2\) $-$ $-$ $+$ $\mathrm{SU}(2)$ \(q+q^{3}+2q^{7}+q^{9}+2q^{11}-6q^{13}+\cdots\)
9600.2.a.bz 9600.a 1.a $1$ $76.656$ \(\Q\) None \(0\) \(1\) \(0\) \(2\) $+$ $-$ $+$ $\mathrm{SU}(2)$ \(q+q^{3}+2q^{7}+q^{9}+4q^{11}+2q^{13}+\cdots\)
9600.2.a.ca 9600.a 1.a $1$ $76.656$ \(\Q\) None \(0\) \(1\) \(0\) \(4\) $-$ $-$ $-$ $\mathrm{SU}(2)$ \(q+q^{3}+4q^{7}+q^{9}-6q^{13}-2q^{17}+\cdots\)
9600.2.a.cb 9600.a 1.a $1$ $76.656$ \(\Q\) None \(0\) \(1\) \(0\) \(4\) $-$ $-$ $-$ $\mathrm{SU}(2)$ \(q+q^{3}+4q^{7}+q^{9}+6q^{13}+2q^{17}+\cdots\)
9600.2.a.cc 9600.a 1.a $1$ $76.656$ \(\Q\) None \(0\) \(1\) \(0\) \(4\) $+$ $-$ $+$ $\mathrm{SU}(2)$ \(q+q^{3}+4q^{7}+q^{9}+2q^{11}+4q^{21}+\cdots\)
9600.2.a.cd 9600.a 1.a $1$ $76.656$ \(\Q\) None \(0\) \(1\) \(0\) \(4\) $+$ $-$ $+$ $\mathrm{SU}(2)$ \(q+q^{3}+4q^{7}+q^{9}+6q^{11}+4q^{13}+\cdots\)
9600.2.a.ce 9600.a 1.a $2$ $76.656$ \(\Q(\sqrt{2}) \) None \(0\) \(-2\) \(0\) \(-2\) $+$ $+$ $-$ $\mathrm{SU}(2)$ \(q-q^{3}+(-1+\beta )q^{7}+q^{9}+(-2+3\beta )q^{11}+\cdots\)
9600.2.a.cf 9600.a 1.a $2$ $76.656$ \(\Q(\sqrt{6}) \) None \(0\) \(-2\) \(0\) \(-2\) $-$ $+$ $+$ $\mathrm{SU}(2)$ \(q-q^{3}+(-1+\beta )q^{7}+q^{9}+(-2-\beta )q^{11}+\cdots\)
9600.2.a.cg 9600.a 1.a $2$ $76.656$ \(\Q(\sqrt{6}) \) None \(0\) \(-2\) \(0\) \(-2\) $-$ $+$ $-$ $\mathrm{SU}(2)$ \(q-q^{3}+(-1+\beta )q^{7}+q^{9}+\beta q^{11}+\cdots\)
9600.2.a.ch 9600.a 1.a $2$ $76.656$ \(\Q(\sqrt{10}) \) None \(0\) \(-2\) \(0\) \(-2\) $-$ $+$ $-$ $\mathrm{SU}(2)$ \(q-q^{3}+(-1+\beta )q^{7}+q^{9}-\beta q^{11}+\cdots\)
9600.2.a.ci 9600.a 1.a $2$ $76.656$ \(\Q(\sqrt{10}) \) None \(0\) \(-2\) \(0\) \(-2\) $+$ $+$ $+$ $\mathrm{SU}(2)$ \(q-q^{3}+(-1+\beta )q^{7}+q^{9}+\beta q^{11}+\cdots\)
9600.2.a.cj 9600.a 1.a $2$ $76.656$ \(\Q(\sqrt{6}) \) None \(0\) \(-2\) \(0\) \(-2\) $+$ $+$ $+$ $\mathrm{SU}(2)$ \(q-q^{3}+(-1+\beta )q^{7}+q^{9}-\beta q^{11}+\cdots\)
9600.2.a.ck 9600.a 1.a $2$ $76.656$ \(\Q(\sqrt{6}) \) None \(0\) \(-2\) \(0\) \(-2\) $-$ $+$ $-$ $\mathrm{SU}(2)$ \(q-q^{3}+(-1+\beta )q^{7}+q^{9}+(2+\beta )q^{11}+\cdots\)
9600.2.a.cl 9600.a 1.a $2$ $76.656$ \(\Q(\sqrt{17}) \) None \(0\) \(-2\) \(0\) \(-2\) $+$ $+$ $+$ $\mathrm{SU}(2)$ \(q-q^{3}+(-1-\beta )q^{7}+q^{9}+2q^{11}+\cdots\)
9600.2.a.cm 9600.a 1.a $2$ $76.656$ \(\Q(\sqrt{2}) \) None \(0\) \(-2\) \(0\) \(-2\) $+$ $+$ $+$ $\mathrm{SU}(2)$ \(q-q^{3}+(-1+\beta )q^{7}+q^{9}+(2-3\beta )q^{11}+\cdots\)
9600.2.a.cn 9600.a 1.a $2$ $76.656$ \(\Q(\sqrt{6}) \) None \(0\) \(-2\) \(0\) \(2\) $-$ $+$ $+$ $\mathrm{SU}(2)$ \(q-q^{3}+(1+\beta )q^{7}+q^{9}+(-2+\beta )q^{11}+\cdots\)
9600.2.a.co 9600.a 1.a $2$ $76.656$ \(\Q(\sqrt{2}) \) None \(0\) \(-2\) \(0\) \(2\) $+$ $+$ $-$ $\mathrm{SU}(2)$ \(q-q^{3}+(1+\beta )q^{7}+q^{9}+(-2-3\beta )q^{11}+\cdots\)
9600.2.a.cp 9600.a 1.a $2$ $76.656$ \(\Q(\sqrt{10}) \) None \(0\) \(-2\) \(0\) \(2\) $+$ $+$ $+$ $\mathrm{SU}(2)$ \(q-q^{3}+(1+\beta )q^{7}+q^{9}-\beta q^{11}-q^{13}+\cdots\)
9600.2.a.cq 9600.a 1.a $2$ $76.656$ \(\Q(\sqrt{6}) \) None \(0\) \(-2\) \(0\) \(2\) $-$ $+$ $+$ $\mathrm{SU}(2)$ \(q-q^{3}+(1+\beta )q^{7}+q^{9}+\beta q^{11}+(-1+\cdots)q^{13}+\cdots\)
9600.2.a.cr 9600.a 1.a $2$ $76.656$ \(\Q(\sqrt{6}) \) None \(0\) \(-2\) \(0\) \(2\) $-$ $+$ $-$ $\mathrm{SU}(2)$ \(q-q^{3}+(1+\beta )q^{7}+q^{9}-\beta q^{11}+(1+\cdots)q^{13}+\cdots\)
9600.2.a.cs 9600.a 1.a $2$ $76.656$ \(\Q(\sqrt{10}) \) None \(0\) \(-2\) \(0\) \(2\) $+$ $+$ $-$ $\mathrm{SU}(2)$ \(q-q^{3}+(1+\beta )q^{7}+q^{9}+\beta q^{11}+q^{13}+\cdots\)
9600.2.a.ct 9600.a 1.a $2$ $76.656$ \(\Q(\sqrt{17}) \) None \(0\) \(-2\) \(0\) \(2\) $-$ $+$ $+$ $\mathrm{SU}(2)$ \(q-q^{3}+(1+\beta )q^{7}+q^{9}+2q^{11}+(1+\cdots)q^{13}+\cdots\)
9600.2.a.cu 9600.a 1.a $2$ $76.656$ \(\Q(\sqrt{2}) \) None \(0\) \(-2\) \(0\) \(2\) $-$ $+$ $+$ $\mathrm{SU}(2)$ \(q-q^{3}+(1+\beta )q^{7}+q^{9}+(2+3\beta )q^{11}+\cdots\)
9600.2.a.cv 9600.a 1.a $2$ $76.656$ \(\Q(\sqrt{6}) \) None \(0\) \(-2\) \(0\) \(2\) $+$ $+$ $-$ $\mathrm{SU}(2)$ \(q-q^{3}+(1+\beta )q^{7}+q^{9}+(2-\beta )q^{11}+\cdots\)
9600.2.a.cw 9600.a 1.a $2$ $76.656$ \(\Q(\sqrt{17}) \) None \(0\) \(2\) \(0\) \(-2\) $-$ $-$ $+$ $\mathrm{SU}(2)$ \(q+q^{3}+(-1-\beta )q^{7}+q^{9}-2q^{11}+\cdots\)
9600.2.a.cx 9600.a 1.a $2$ $76.656$ \(\Q(\sqrt{2}) \) None \(0\) \(2\) \(0\) \(-2\) $-$ $-$ $+$ $\mathrm{SU}(2)$ \(q+q^{3}+(-1+\beta )q^{7}+q^{9}+(-2+3\beta )q^{11}+\cdots\)
9600.2.a.cy 9600.a 1.a $2$ $76.656$ \(\Q(\sqrt{6}) \) None \(0\) \(2\) \(0\) \(-2\) $+$ $-$ $-$ $\mathrm{SU}(2)$ \(q+q^{3}+(-1+\beta )q^{7}+q^{9}+(-2-\beta )q^{11}+\cdots\)
9600.2.a.cz 9600.a 1.a $2$ $76.656$ \(\Q(\sqrt{10}) \) None \(0\) \(2\) \(0\) \(-2\) $-$ $-$ $+$ $\mathrm{SU}(2)$ \(q+q^{3}+(-1+\beta )q^{7}+q^{9}-\beta q^{11}+\cdots\)
9600.2.a.da 9600.a 1.a $2$ $76.656$ \(\Q(\sqrt{6}) \) None \(0\) \(2\) \(0\) \(-2\) $+$ $-$ $+$ $\mathrm{SU}(2)$ \(q+q^{3}+(-1+\beta )q^{7}+q^{9}+\beta q^{11}+\cdots\)
9600.2.a.db 9600.a 1.a $2$ $76.656$ \(\Q(\sqrt{6}) \) None \(0\) \(2\) \(0\) \(-2\) $+$ $-$ $-$ $\mathrm{SU}(2)$ \(q+q^{3}+(-1+\beta )q^{7}+q^{9}-\beta q^{11}+\cdots\)
9600.2.a.dc 9600.a 1.a $2$ $76.656$ \(\Q(\sqrt{10}) \) None \(0\) \(2\) \(0\) \(-2\) $-$ $-$ $-$ $\mathrm{SU}(2)$ \(q+q^{3}+(-1+\beta )q^{7}+q^{9}+\beta q^{11}+\cdots\)
9600.2.a.dd 9600.a 1.a $2$ $76.656$ \(\Q(\sqrt{6}) \) None \(0\) \(2\) \(0\) \(-2\) $-$ $-$ $+$ $\mathrm{SU}(2)$ \(q+q^{3}+(-1+\beta )q^{7}+q^{9}+(2+\beta )q^{11}+\cdots\)
9600.2.a.de 9600.a 1.a $2$ $76.656$ \(\Q(\sqrt{2}) \) None \(0\) \(2\) \(0\) \(-2\) $+$ $-$ $-$ $\mathrm{SU}(2)$ \(q+q^{3}+(-1+\beta )q^{7}+q^{9}+(2-3\beta )q^{11}+\cdots\)
9600.2.a.df 9600.a 1.a $2$ $76.656$ \(\Q(\sqrt{6}) \) None \(0\) \(2\) \(0\) \(2\) $+$ $-$ $-$ $\mathrm{SU}(2)$ \(q+q^{3}+(1+\beta )q^{7}+q^{9}+(-2+\beta )q^{11}+\cdots\)
9600.2.a.dg 9600.a 1.a $2$ $76.656$ \(\Q(\sqrt{17}) \) None \(0\) \(2\) \(0\) \(2\) $-$ $-$ $+$ $\mathrm{SU}(2)$ \(q+q^{3}+(1+\beta )q^{7}+q^{9}-2q^{11}+(-1+\cdots)q^{13}+\cdots\)
9600.2.a.dh 9600.a 1.a $2$ $76.656$ \(\Q(\sqrt{2}) \) None \(0\) \(2\) \(0\) \(2\) $-$ $-$ $+$ $\mathrm{SU}(2)$ \(q+q^{3}+(1+\beta )q^{7}+q^{9}+(-2-3\beta )q^{11}+\cdots\)
9600.2.a.di 9600.a 1.a $2$ $76.656$ \(\Q(\sqrt{6}) \) None \(0\) \(2\) \(0\) \(2\) $-$ $-$ $-$ $\mathrm{SU}(2)$ \(q+q^{3}+(1+\beta )q^{7}+q^{9}+\beta q^{11}+(-1+\cdots)q^{13}+\cdots\)
9600.2.a.dj 9600.a 1.a $2$ $76.656$ \(\Q(\sqrt{10}) \) None \(0\) \(2\) \(0\) \(2\) $-$ $-$ $-$ $\mathrm{SU}(2)$ \(q+q^{3}+(1+\beta )q^{7}+q^{9}-\beta q^{11}-q^{13}+\cdots\)
9600.2.a.dk 9600.a 1.a $2$ $76.656$ \(\Q(\sqrt{10}) \) None \(0\) \(2\) \(0\) \(2\) $+$ $-$ $+$ $\mathrm{SU}(2)$ \(q+q^{3}+(1+\beta )q^{7}+q^{9}+\beta q^{11}+q^{13}+\cdots\)
9600.2.a.dl 9600.a 1.a $2$ $76.656$ \(\Q(\sqrt{6}) \) None \(0\) \(2\) \(0\) \(2\) $+$ $-$ $+$ $\mathrm{SU}(2)$ \(q+q^{3}+(1+\beta )q^{7}+q^{9}-\beta q^{11}+(1+\cdots)q^{13}+\cdots\)
9600.2.a.dm 9600.a 1.a $2$ $76.656$ \(\Q(\sqrt{2}) \) None \(0\) \(2\) \(0\) \(2\) $-$ $-$ $-$ $\mathrm{SU}(2)$ \(q+q^{3}+(1+\beta )q^{7}+q^{9}+(2+3\beta )q^{11}+\cdots\)
9600.2.a.dn 9600.a 1.a $2$ $76.656$ \(\Q(\sqrt{6}) \) None \(0\) \(2\) \(0\) \(2\) $+$ $-$ $+$ $\mathrm{SU}(2)$ \(q+q^{3}+(1+\beta )q^{7}+q^{9}+(2-\beta )q^{11}+\cdots\)
9600.2.a.do 9600.a 1.a $3$ $76.656$ 3.3.148.1 None \(0\) \(-3\) \(0\) \(-4\) $-$ $+$ $-$ $\mathrm{SU}(2)$ \(q-q^{3}+(-1+\beta _{1})q^{7}+q^{9}+(-2-\beta _{2})q^{11}+\cdots\)
9600.2.a.dp 9600.a 1.a $3$ $76.656$ 3.3.148.1 None \(0\) \(-3\) \(0\) \(-4\) $+$ $+$ $-$ $\mathrm{SU}(2)$ \(q-q^{3}+(-1+\beta _{1})q^{7}+q^{9}+(2+\beta _{2})q^{11}+\cdots\)
9600.2.a.dq 9600.a 1.a $3$ $76.656$ 3.3.148.1 None \(0\) \(-3\) \(0\) \(4\) $+$ $+$ $-$ $\mathrm{SU}(2)$ \(q-q^{3}+(1-\beta _{1})q^{7}+q^{9}+(-2-\beta _{2})q^{11}+\cdots\)
9600.2.a.dr 9600.a 1.a $3$ $76.656$ 3.3.148.1 None \(0\) \(-3\) \(0\) \(4\) $+$ $+$ $-$ $\mathrm{SU}(2)$ \(q-q^{3}+(1-\beta _{1})q^{7}+q^{9}+(2+\beta _{2})q^{11}+\cdots\)
9600.2.a.ds 9600.a 1.a $3$ $76.656$ 3.3.148.1 None \(0\) \(3\) \(0\) \(-4\) $-$ $-$ $-$ $\mathrm{SU}(2)$ \(q+q^{3}+(-1+\beta _{1})q^{7}+q^{9}+(-2-\beta _{2})q^{11}+\cdots\)
9600.2.a.dt 9600.a 1.a $3$ $76.656$ 3.3.148.1 None \(0\) \(3\) \(0\) \(-4\) $-$ $-$ $-$ $\mathrm{SU}(2)$ \(q+q^{3}+(-1+\beta _{1})q^{7}+q^{9}+(2+\beta _{2})q^{11}+\cdots\)
9600.2.a.du 9600.a 1.a $3$ $76.656$ 3.3.148.1 None \(0\) \(3\) \(0\) \(4\) $+$ $-$ $-$ $\mathrm{SU}(2)$ \(q+q^{3}+(1-\beta _{1})q^{7}+q^{9}+(-2-\beta _{2})q^{11}+\cdots\)
9600.2.a.dv 9600.a 1.a $3$ $76.656$ 3.3.148.1 None \(0\) \(3\) \(0\) \(4\) $-$ $-$ $-$ $\mathrm{SU}(2)$ \(q+q^{3}+(1-\beta _{1})q^{7}+q^{9}+(2+\beta _{2})q^{11}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_0(9600))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_0(9600)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_0(15))\)\(^{\oplus 16}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(20))\)\(^{\oplus 24}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(24))\)\(^{\oplus 15}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(30))\)\(^{\oplus 14}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(32))\)\(^{\oplus 18}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(40))\)\(^{\oplus 20}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(48))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(50))\)\(^{\oplus 14}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(64))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(75))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(80))\)\(^{\oplus 16}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(96))\)\(^{\oplus 9}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(100))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(120))\)\(^{\oplus 10}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(128))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(150))\)\(^{\oplus 7}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(160))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(192))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(200))\)\(^{\oplus 10}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(240))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(300))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(320))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(384))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(400))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(480))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(600))\)\(^{\oplus 5}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(640))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(800))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(960))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(1200))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(1600))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(1920))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(2400))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(3200))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(4800))\)\(^{\oplus 2}\)