Properties

Label 9360.2.a
Level $9360$
Weight $2$
Character orbit 9360.a
Rep. character $\chi_{9360}(1,\cdot)$
Character field $\Q$
Dimension $120$
Newform subspaces $83$
Sturm bound $4032$
Trace bound $19$

Related objects

Downloads

Learn more

Defining parameters

Level: \( N \) \(=\) \( 9360 = 2^{4} \cdot 3^{2} \cdot 5 \cdot 13 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 9360.a (trivial)
Character field: \(\Q\)
Newform subspaces: \( 83 \)
Sturm bound: \(4032\)
Trace bound: \(19\)
Distinguishing \(T_p\): \(7\), \(11\), \(17\), \(19\), \(31\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_0(9360))\).

Total New Old
Modular forms 2064 120 1944
Cusp forms 1969 120 1849
Eisenstein series 95 0 95

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

\(2\)\(3\)\(5\)\(13\)FrickeDim.
\(+\)\(+\)\(+\)\(+\)\(+\)\(7\)
\(+\)\(+\)\(+\)\(-\)\(-\)\(5\)
\(+\)\(+\)\(-\)\(+\)\(-\)\(7\)
\(+\)\(+\)\(-\)\(-\)\(+\)\(5\)
\(+\)\(-\)\(+\)\(+\)\(-\)\(9\)
\(+\)\(-\)\(+\)\(-\)\(+\)\(8\)
\(+\)\(-\)\(-\)\(+\)\(+\)\(8\)
\(+\)\(-\)\(-\)\(-\)\(-\)\(11\)
\(-\)\(+\)\(+\)\(+\)\(-\)\(5\)
\(-\)\(+\)\(+\)\(-\)\(+\)\(7\)
\(-\)\(+\)\(-\)\(+\)\(+\)\(5\)
\(-\)\(+\)\(-\)\(-\)\(-\)\(7\)
\(-\)\(-\)\(+\)\(+\)\(+\)\(9\)
\(-\)\(-\)\(+\)\(-\)\(-\)\(10\)
\(-\)\(-\)\(-\)\(+\)\(-\)\(10\)
\(-\)\(-\)\(-\)\(-\)\(+\)\(7\)
Plus space\(+\)\(56\)
Minus space\(-\)\(64\)

Trace form

\( 120 q + 4 q^{7} + O(q^{10}) \) \( 120 q + 4 q^{7} + 8 q^{11} - 8 q^{17} - 8 q^{19} + 8 q^{23} + 120 q^{25} - 24 q^{29} - 8 q^{31} - 16 q^{37} + 8 q^{41} + 8 q^{43} - 20 q^{47} + 120 q^{49} - 8 q^{53} + 24 q^{61} - 4 q^{67} - 16 q^{71} + 24 q^{73} - 8 q^{77} - 28 q^{83} + 16 q^{85} + 24 q^{97} + O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(9360))\) 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 13
9360.2.a.a 9360.a 1.a $1$ $74.740$ \(\Q\) None \(0\) \(0\) \(-1\) \(-4\) $+$ $-$ $+$ $-$ $\mathrm{SU}(2)$ \(q-q^{5}-4q^{7}+q^{13}-2q^{17}+q^{25}+\cdots\)
9360.2.a.b 9360.a 1.a $1$ $74.740$ \(\Q\) None \(0\) \(0\) \(-1\) \(-4\) $+$ $-$ $+$ $-$ $\mathrm{SU}(2)$ \(q-q^{5}-4q^{7}+4q^{11}+q^{13}-6q^{17}+\cdots\)
9360.2.a.c 9360.a 1.a $1$ $74.740$ \(\Q\) None \(0\) \(0\) \(-1\) \(-3\) $+$ $+$ $+$ $+$ $\mathrm{SU}(2)$ \(q-q^{5}-3q^{7}-5q^{11}-q^{13}-3q^{17}+\cdots\)
9360.2.a.d 9360.a 1.a $1$ $74.740$ \(\Q\) None \(0\) \(0\) \(-1\) \(-3\) $-$ $-$ $+$ $+$ $\mathrm{SU}(2)$ \(q-q^{5}-3q^{7}-q^{11}-q^{13}+q^{17}+\cdots\)
9360.2.a.e 9360.a 1.a $1$ $74.740$ \(\Q\) None \(0\) \(0\) \(-1\) \(-3\) $-$ $-$ $+$ $-$ $\mathrm{SU}(2)$ \(q-q^{5}-3q^{7}+q^{11}+q^{13}+3q^{17}+\cdots\)
9360.2.a.f 9360.a 1.a $1$ $74.740$ \(\Q\) None \(0\) \(0\) \(-1\) \(-2\) $-$ $+$ $+$ $+$ $\mathrm{SU}(2)$ \(q-q^{5}-2q^{7}-4q^{11}-q^{13}-4q^{17}+\cdots\)
9360.2.a.g 9360.a 1.a $1$ $74.740$ \(\Q\) None \(0\) \(0\) \(-1\) \(-2\) $-$ $-$ $+$ $-$ $\mathrm{SU}(2)$ \(q-q^{5}-2q^{7}+q^{13}-2q^{19}-6q^{23}+\cdots\)
9360.2.a.h 9360.a 1.a $1$ $74.740$ \(\Q\) None \(0\) \(0\) \(-1\) \(-2\) $+$ $+$ $+$ $+$ $\mathrm{SU}(2)$ \(q-q^{5}-2q^{7}+4q^{11}-q^{13}-8q^{17}+\cdots\)
9360.2.a.i 9360.a 1.a $1$ $74.740$ \(\Q\) None \(0\) \(0\) \(-1\) \(-2\) $-$ $+$ $+$ $+$ $\mathrm{SU}(2)$ \(q-q^{5}-2q^{7}+4q^{11}-q^{13}-4q^{17}+\cdots\)
9360.2.a.j 9360.a 1.a $1$ $74.740$ \(\Q\) None \(0\) \(0\) \(-1\) \(-2\) $+$ $-$ $+$ $+$ $\mathrm{SU}(2)$ \(q-q^{5}-2q^{7}+4q^{11}-q^{13}-2q^{19}+\cdots\)
9360.2.a.k 9360.a 1.a $1$ $74.740$ \(\Q\) None \(0\) \(0\) \(-1\) \(0\) $+$ $-$ $+$ $-$ $\mathrm{SU}(2)$ \(q-q^{5}-4q^{11}+q^{13}-2q^{17}+4q^{19}+\cdots\)
9360.2.a.l 9360.a 1.a $1$ $74.740$ \(\Q\) None \(0\) \(0\) \(-1\) \(0\) $-$ $-$ $+$ $-$ $\mathrm{SU}(2)$ \(q-q^{5}+q^{13}-2q^{17}+8q^{19}-4q^{23}+\cdots\)
9360.2.a.m 9360.a 1.a $1$ $74.740$ \(\Q\) None \(0\) \(0\) \(-1\) \(0\) $+$ $+$ $+$ $-$ $\mathrm{SU}(2)$ \(q-q^{5}+q^{13}+6q^{17}+8q^{19}+6q^{23}+\cdots\)
9360.2.a.n 9360.a 1.a $1$ $74.740$ \(\Q\) None \(0\) \(0\) \(-1\) \(0\) $+$ $-$ $+$ $-$ $\mathrm{SU}(2)$ \(q-q^{5}+2q^{11}+q^{13}-2q^{17}-2q^{19}+\cdots\)
9360.2.a.o 9360.a 1.a $1$ $74.740$ \(\Q\) None \(0\) \(0\) \(-1\) \(0\) $-$ $-$ $+$ $-$ $\mathrm{SU}(2)$ \(q-q^{5}+4q^{11}+q^{13}-2q^{17}+4q^{19}+\cdots\)
9360.2.a.p 9360.a 1.a $1$ $74.740$ \(\Q\) None \(0\) \(0\) \(-1\) \(0\) $-$ $-$ $+$ $-$ $\mathrm{SU}(2)$ \(q-q^{5}+4q^{11}+q^{13}+6q^{17}-4q^{19}+\cdots\)
9360.2.a.q 9360.a 1.a $1$ $74.740$ \(\Q\) None \(0\) \(0\) \(-1\) \(0\) $-$ $+$ $+$ $-$ $\mathrm{SU}(2)$ \(q-q^{5}+6q^{11}+q^{13}+4q^{17}-4q^{19}+\cdots\)
9360.2.a.r 9360.a 1.a $1$ $74.740$ \(\Q\) None \(0\) \(0\) \(-1\) \(1\) $-$ $+$ $+$ $-$ $\mathrm{SU}(2)$ \(q-q^{5}+q^{7}-3q^{11}+q^{13}+3q^{17}+\cdots\)
9360.2.a.s 9360.a 1.a $1$ $74.740$ \(\Q\) None \(0\) \(0\) \(-1\) \(1\) $-$ $+$ $+$ $+$ $\mathrm{SU}(2)$ \(q-q^{5}+q^{7}-q^{11}-q^{13}+5q^{17}+\cdots\)
9360.2.a.t 9360.a 1.a $1$ $74.740$ \(\Q\) None \(0\) \(0\) \(-1\) \(2\) $-$ $-$ $+$ $+$ $\mathrm{SU}(2)$ \(q-q^{5}+2q^{7}-2q^{11}-q^{13}+2q^{17}+\cdots\)
9360.2.a.u 9360.a 1.a $1$ $74.740$ \(\Q\) None \(0\) \(0\) \(-1\) \(2\) $+$ $-$ $+$ $-$ $\mathrm{SU}(2)$ \(q-q^{5}+2q^{7}+q^{13}+4q^{17}-6q^{19}+\cdots\)
9360.2.a.v 9360.a 1.a $1$ $74.740$ \(\Q\) None \(0\) \(0\) \(-1\) \(2\) $-$ $-$ $+$ $+$ $\mathrm{SU}(2)$ \(q-q^{5}+2q^{7}+4q^{11}-q^{13}-4q^{17}+\cdots\)
9360.2.a.w 9360.a 1.a $1$ $74.740$ \(\Q\) None \(0\) \(0\) \(-1\) \(3\) $-$ $-$ $+$ $-$ $\mathrm{SU}(2)$ \(q-q^{5}+3q^{7}-5q^{11}+q^{13}-5q^{17}+\cdots\)
9360.2.a.x 9360.a 1.a $1$ $74.740$ \(\Q\) None \(0\) \(0\) \(-1\) \(3\) $+$ $-$ $+$ $+$ $\mathrm{SU}(2)$ \(q-q^{5}+3q^{7}-3q^{11}-q^{13}+q^{17}+\cdots\)
9360.2.a.y 9360.a 1.a $1$ $74.740$ \(\Q\) None \(0\) \(0\) \(-1\) \(3\) $+$ $+$ $+$ $-$ $\mathrm{SU}(2)$ \(q-q^{5}+3q^{7}+3q^{11}+q^{13}+3q^{17}+\cdots\)
9360.2.a.z 9360.a 1.a $1$ $74.740$ \(\Q\) None \(0\) \(0\) \(-1\) \(4\) $-$ $-$ $+$ $-$ $\mathrm{SU}(2)$ \(q-q^{5}+4q^{7}-6q^{11}+q^{13}+6q^{17}+\cdots\)
9360.2.a.ba 9360.a 1.a $1$ $74.740$ \(\Q\) None \(0\) \(0\) \(-1\) \(4\) $-$ $+$ $+$ $-$ $\mathrm{SU}(2)$ \(q-q^{5}+4q^{7}+q^{13}-6q^{17}+4q^{19}+\cdots\)
9360.2.a.bb 9360.a 1.a $1$ $74.740$ \(\Q\) None \(0\) \(0\) \(-1\) \(5\) $+$ $-$ $+$ $-$ $\mathrm{SU}(2)$ \(q-q^{5}+5q^{7}+q^{11}+q^{13}+3q^{17}+\cdots\)
9360.2.a.bc 9360.a 1.a $1$ $74.740$ \(\Q\) None \(0\) \(0\) \(1\) \(-4\) $-$ $-$ $-$ $+$ $\mathrm{SU}(2)$ \(q+q^{5}-4q^{7}-q^{13}+2q^{17}-4q^{19}+\cdots\)
9360.2.a.bd 9360.a 1.a $1$ $74.740$ \(\Q\) None \(0\) \(0\) \(1\) \(-3\) $+$ $+$ $-$ $+$ $\mathrm{SU}(2)$ \(q+q^{5}-3q^{7}+5q^{11}-q^{13}+3q^{17}+\cdots\)
9360.2.a.be 9360.a 1.a $1$ $74.740$ \(\Q\) None \(0\) \(0\) \(1\) \(-2\) $-$ $+$ $-$ $+$ $\mathrm{SU}(2)$ \(q+q^{5}-2q^{7}-4q^{11}-q^{13}+4q^{17}+\cdots\)
9360.2.a.bf 9360.a 1.a $1$ $74.740$ \(\Q\) None \(0\) \(0\) \(1\) \(-2\) $+$ $+$ $-$ $+$ $\mathrm{SU}(2)$ \(q+q^{5}-2q^{7}-4q^{11}-q^{13}+8q^{17}+\cdots\)
9360.2.a.bg 9360.a 1.a $1$ $74.740$ \(\Q\) None \(0\) \(0\) \(1\) \(-2\) $-$ $-$ $-$ $-$ $\mathrm{SU}(2)$ \(q+q^{5}-2q^{7}+q^{13}-2q^{19}-6q^{23}+\cdots\)
9360.2.a.bh 9360.a 1.a $1$ $74.740$ \(\Q\) None \(0\) \(0\) \(1\) \(-2\) $-$ $-$ $-$ $+$ $\mathrm{SU}(2)$ \(q+q^{5}-2q^{7}+4q^{11}-q^{13}-8q^{17}+\cdots\)
9360.2.a.bi 9360.a 1.a $1$ $74.740$ \(\Q\) None \(0\) \(0\) \(1\) \(-2\) $-$ $-$ $-$ $+$ $\mathrm{SU}(2)$ \(q+q^{5}-2q^{7}+4q^{11}-q^{13}-2q^{17}+\cdots\)
9360.2.a.bj 9360.a 1.a $1$ $74.740$ \(\Q\) None \(0\) \(0\) \(1\) \(-2\) $-$ $+$ $-$ $+$ $\mathrm{SU}(2)$ \(q+q^{5}-2q^{7}+4q^{11}-q^{13}+4q^{17}+\cdots\)
9360.2.a.bk 9360.a 1.a $1$ $74.740$ \(\Q\) None \(0\) \(0\) \(1\) \(0\) $-$ $+$ $-$ $-$ $\mathrm{SU}(2)$ \(q+q^{5}-6q^{11}+q^{13}-4q^{17}-4q^{19}+\cdots\)
9360.2.a.bl 9360.a 1.a $1$ $74.740$ \(\Q\) None \(0\) \(0\) \(1\) \(0\) $+$ $-$ $-$ $+$ $\mathrm{SU}(2)$ \(q+q^{5}-4q^{11}-q^{13}+6q^{17}-4q^{19}+\cdots\)
9360.2.a.bm 9360.a 1.a $1$ $74.740$ \(\Q\) None \(0\) \(0\) \(1\) \(0\) $+$ $-$ $-$ $+$ $\mathrm{SU}(2)$ \(q+q^{5}-q^{13}-2q^{17}+4q^{23}+q^{25}+\cdots\)
9360.2.a.bn 9360.a 1.a $1$ $74.740$ \(\Q\) None \(0\) \(0\) \(1\) \(0\) $-$ $-$ $-$ $+$ $\mathrm{SU}(2)$ \(q+q^{5}-q^{13}+6q^{17}-4q^{23}+q^{25}+\cdots\)
9360.2.a.bo 9360.a 1.a $1$ $74.740$ \(\Q\) None \(0\) \(0\) \(1\) \(0\) $+$ $+$ $-$ $-$ $\mathrm{SU}(2)$ \(q+q^{5}+q^{13}-6q^{17}+8q^{19}-6q^{23}+\cdots\)
9360.2.a.bp 9360.a 1.a $1$ $74.740$ \(\Q\) None \(0\) \(0\) \(1\) \(0\) $+$ $-$ $-$ $-$ $\mathrm{SU}(2)$ \(q+q^{5}+q^{13}+6q^{17}-4q^{19}+q^{25}+\cdots\)
9360.2.a.bq 9360.a 1.a $1$ $74.740$ \(\Q\) None \(0\) \(0\) \(1\) \(0\) $+$ $-$ $-$ $-$ $\mathrm{SU}(2)$ \(q+q^{5}+4q^{11}+q^{13}+2q^{17}+4q^{19}+\cdots\)
9360.2.a.br 9360.a 1.a $1$ $74.740$ \(\Q\) None \(0\) \(0\) \(1\) \(1\) $+$ $-$ $-$ $-$ $\mathrm{SU}(2)$ \(q+q^{5}+q^{7}-5q^{11}+q^{13}-3q^{17}+\cdots\)
9360.2.a.bs 9360.a 1.a $1$ $74.740$ \(\Q\) None \(0\) \(0\) \(1\) \(1\) $-$ $+$ $-$ $+$ $\mathrm{SU}(2)$ \(q+q^{5}+q^{7}+q^{11}-q^{13}-5q^{17}+\cdots\)
9360.2.a.bt 9360.a 1.a $1$ $74.740$ \(\Q\) None \(0\) \(0\) \(1\) \(1\) $-$ $-$ $-$ $-$ $\mathrm{SU}(2)$ \(q+q^{5}+q^{7}+3q^{11}+q^{13}-3q^{17}+\cdots\)
9360.2.a.bu 9360.a 1.a $1$ $74.740$ \(\Q\) None \(0\) \(0\) \(1\) \(1\) $-$ $+$ $-$ $-$ $\mathrm{SU}(2)$ \(q+q^{5}+q^{7}+3q^{11}+q^{13}-3q^{17}+\cdots\)
9360.2.a.bv 9360.a 1.a $1$ $74.740$ \(\Q\) None \(0\) \(0\) \(1\) \(1\) $-$ $-$ $-$ $+$ $\mathrm{SU}(2)$ \(q+q^{5}+q^{7}+5q^{11}-q^{13}+7q^{17}+\cdots\)
9360.2.a.bw 9360.a 1.a $1$ $74.740$ \(\Q\) None \(0\) \(0\) \(1\) \(2\) $-$ $-$ $-$ $+$ $\mathrm{SU}(2)$ \(q+q^{5}+2q^{7}-6q^{11}-q^{13}+2q^{17}+\cdots\)
9360.2.a.bx 9360.a 1.a $1$ $74.740$ \(\Q\) None \(0\) \(0\) \(1\) \(3\) $+$ $+$ $-$ $-$ $\mathrm{SU}(2)$ \(q+q^{5}+3q^{7}-3q^{11}+q^{13}-3q^{17}+\cdots\)
9360.2.a.by 9360.a 1.a $1$ $74.740$ \(\Q\) None \(0\) \(0\) \(1\) \(4\) $-$ $-$ $-$ $+$ $\mathrm{SU}(2)$ \(q+q^{5}+4q^{7}-2q^{11}-q^{13}-2q^{17}+\cdots\)
9360.2.a.bz 9360.a 1.a $1$ $74.740$ \(\Q\) None \(0\) \(0\) \(1\) \(4\) $-$ $+$ $-$ $-$ $\mathrm{SU}(2)$ \(q+q^{5}+4q^{7}+q^{13}+6q^{17}+4q^{19}+\cdots\)
9360.2.a.ca 9360.a 1.a $1$ $74.740$ \(\Q\) None \(0\) \(0\) \(1\) \(4\) $-$ $-$ $-$ $+$ $\mathrm{SU}(2)$ \(q+q^{5}+4q^{7}+2q^{11}-q^{13}-2q^{17}+\cdots\)
9360.2.a.cb 9360.a 1.a $1$ $74.740$ \(\Q\) None \(0\) \(0\) \(1\) \(4\) $+$ $-$ $-$ $-$ $\mathrm{SU}(2)$ \(q+q^{5}+4q^{7}+4q^{11}+q^{13}+6q^{17}+\cdots\)
9360.2.a.cc 9360.a 1.a $2$ $74.740$ \(\Q(\sqrt{6}) \) None \(0\) \(0\) \(-2\) \(-4\) $+$ $-$ $+$ $+$ $\mathrm{SU}(2)$ \(q-q^{5}-2q^{7}+(-2+\beta )q^{11}-q^{13}+\cdots\)
9360.2.a.cd 9360.a 1.a $2$ $74.740$ \(\Q(\sqrt{2}) \) None \(0\) \(0\) \(-2\) \(-4\) $-$ $-$ $+$ $+$ $\mathrm{SU}(2)$ \(q-q^{5}+(-2+2\beta )q^{7}+(2-\beta )q^{11}+\cdots\)
9360.2.a.ce 9360.a 1.a $2$ $74.740$ \(\Q(\sqrt{17}) \) None \(0\) \(0\) \(-2\) \(-3\) $-$ $-$ $+$ $+$ $\mathrm{SU}(2)$ \(q-q^{5}+(-1-\beta )q^{7}+(1+\beta )q^{11}-q^{13}+\cdots\)
9360.2.a.cf 9360.a 1.a $2$ $74.740$ \(\Q(\sqrt{13}) \) None \(0\) \(0\) \(-2\) \(-2\) $-$ $+$ $+$ $-$ $\mathrm{SU}(2)$ \(q-q^{5}+(-1-\beta )q^{7}+q^{13}+(-1+\beta )q^{17}+\cdots\)
9360.2.a.cg 9360.a 1.a $2$ $74.740$ \(\Q(\sqrt{33}) \) None \(0\) \(0\) \(-2\) \(-1\) $-$ $+$ $+$ $-$ $\mathrm{SU}(2)$ \(q-q^{5}-\beta q^{7}+(-2+\beta )q^{11}+q^{13}+\cdots\)
9360.2.a.ch 9360.a 1.a $2$ $74.740$ \(\Q(\sqrt{2}) \) None \(0\) \(0\) \(-2\) \(0\) $-$ $-$ $+$ $+$ $\mathrm{SU}(2)$ \(q-q^{5}+\beta q^{7}+2\beta q^{11}-q^{13}+(2-\beta )q^{17}+\cdots\)
9360.2.a.ci 9360.a 1.a $2$ $74.740$ \(\Q(\sqrt{17}) \) None \(0\) \(0\) \(-2\) \(1\) $+$ $-$ $+$ $-$ $\mathrm{SU}(2)$ \(q-q^{5}+\beta q^{7}+(-4+\beta )q^{11}+q^{13}+\cdots\)
9360.2.a.cj 9360.a 1.a $2$ $74.740$ \(\Q(\sqrt{5}) \) None \(0\) \(0\) \(-2\) \(4\) $+$ $+$ $+$ $+$ $\mathrm{SU}(2)$ \(q-q^{5}+2q^{7}-q^{13}+(2+\beta )q^{17}-2q^{19}+\cdots\)
9360.2.a.ck 9360.a 1.a $2$ $74.740$ \(\Q(\sqrt{2}) \) None \(0\) \(0\) \(-2\) \(4\) $+$ $-$ $+$ $+$ $\mathrm{SU}(2)$ \(q-q^{5}+2q^{7}-3\beta q^{11}-q^{13}+(2-2\beta )q^{17}+\cdots\)
9360.2.a.cl 9360.a 1.a $2$ $74.740$ \(\Q(\sqrt{17}) \) None \(0\) \(0\) \(-2\) \(5\) $-$ $+$ $+$ $+$ $\mathrm{SU}(2)$ \(q-q^{5}+(3-\beta )q^{7}+(1-\beta )q^{11}-q^{13}+\cdots\)
9360.2.a.cm 9360.a 1.a $2$ $74.740$ \(\Q(\sqrt{3}) \) None \(0\) \(0\) \(2\) \(-4\) $-$ $-$ $-$ $-$ $\mathrm{SU}(2)$ \(q+q^{5}-2q^{7}+(-3+\beta )q^{11}+q^{13}+\cdots\)
9360.2.a.cn 9360.a 1.a $2$ $74.740$ \(\Q(\sqrt{13}) \) None \(0\) \(0\) \(2\) \(-2\) $-$ $+$ $-$ $-$ $\mathrm{SU}(2)$ \(q+q^{5}+(-1-\beta )q^{7}+q^{13}+(1-\beta )q^{17}+\cdots\)
9360.2.a.co 9360.a 1.a $2$ $74.740$ \(\Q(\sqrt{33}) \) None \(0\) \(0\) \(2\) \(-1\) $+$ $-$ $-$ $+$ $\mathrm{SU}(2)$ \(q+q^{5}-\beta q^{7}-\beta q^{11}-q^{13}+(-2+\cdots)q^{17}+\cdots\)
9360.2.a.cp 9360.a 1.a $2$ $74.740$ \(\Q(\sqrt{33}) \) None \(0\) \(0\) \(2\) \(-1\) $-$ $+$ $-$ $-$ $\mathrm{SU}(2)$ \(q+q^{5}-\beta q^{7}+(2-\beta )q^{11}+q^{13}+(4+\cdots)q^{17}+\cdots\)
9360.2.a.cq 9360.a 1.a $2$ $74.740$ \(\Q(\sqrt{3}) \) None \(0\) \(0\) \(2\) \(0\) $+$ $-$ $-$ $-$ $\mathrm{SU}(2)$ \(q+q^{5}+2\beta q^{7}+(-3+\beta )q^{11}+q^{13}+\cdots\)
9360.2.a.cr 9360.a 1.a $2$ $74.740$ \(\Q(\sqrt{3}) \) None \(0\) \(0\) \(2\) \(0\) $+$ $-$ $-$ $-$ $\mathrm{SU}(2)$ \(q+q^{5}+2\beta q^{7}+(1-\beta )q^{11}+q^{13}+\cdots\)
9360.2.a.cs 9360.a 1.a $2$ $74.740$ \(\Q(\sqrt{5}) \) None \(0\) \(0\) \(2\) \(0\) $+$ $-$ $-$ $+$ $\mathrm{SU}(2)$ \(q+q^{5}+(3+\beta )q^{11}-q^{13}-2q^{17}+\cdots\)
9360.2.a.ct 9360.a 1.a $2$ $74.740$ \(\Q(\sqrt{41}) \) None \(0\) \(0\) \(2\) \(1\) $+$ $-$ $-$ $+$ $\mathrm{SU}(2)$ \(q+q^{5}+\beta q^{7}+(-2-\beta )q^{11}-q^{13}+\cdots\)
9360.2.a.cu 9360.a 1.a $2$ $74.740$ \(\Q(\sqrt{73}) \) None \(0\) \(0\) \(2\) \(1\) $-$ $-$ $-$ $+$ $\mathrm{SU}(2)$ \(q+q^{5}+\beta q^{7}+\beta q^{11}-q^{13}+\beta q^{17}+\cdots\)
9360.2.a.cv 9360.a 1.a $2$ $74.740$ \(\Q(\sqrt{5}) \) None \(0\) \(0\) \(2\) \(4\) $+$ $+$ $-$ $+$ $\mathrm{SU}(2)$ \(q+q^{5}+2q^{7}-q^{13}+(-2-\beta )q^{17}+\cdots\)
9360.2.a.cw 9360.a 1.a $2$ $74.740$ \(\Q(\sqrt{17}) \) None \(0\) \(0\) \(2\) \(5\) $-$ $+$ $-$ $+$ $\mathrm{SU}(2)$ \(q+q^{5}+(3-\beta )q^{7}+(-1+\beta )q^{11}-q^{13}+\cdots\)
9360.2.a.cx 9360.a 1.a $3$ $74.740$ 3.3.621.1 None \(0\) \(0\) \(-3\) \(-3\) $+$ $+$ $+$ $-$ $\mathrm{SU}(2)$ \(q-q^{5}+(-1-\beta _{2})q^{7}+(1-\beta _{1}-\beta _{2})q^{11}+\cdots\)
9360.2.a.cy 9360.a 1.a $3$ $74.740$ 3.3.940.1 None \(0\) \(0\) \(-3\) \(-1\) $+$ $-$ $+$ $+$ $\mathrm{SU}(2)$ \(q-q^{5}-\beta _{2}q^{7}+(2+\beta _{1})q^{11}-q^{13}+\cdots\)
9360.2.a.cz 9360.a 1.a $3$ $74.740$ 3.3.1016.1 None \(0\) \(0\) \(-3\) \(1\) $+$ $+$ $+$ $+$ $\mathrm{SU}(2)$ \(q-q^{5}+\beta _{2}q^{7}+(-2+\beta _{1})q^{11}-q^{13}+\cdots\)
9360.2.a.da 9360.a 1.a $3$ $74.740$ 3.3.564.1 None \(0\) \(0\) \(-3\) \(2\) $-$ $-$ $+$ $-$ $\mathrm{SU}(2)$ \(q-q^{5}+(1+\beta _{1})q^{7}+(\beta _{1}-\beta _{2})q^{11}+\cdots\)
9360.2.a.db 9360.a 1.a $3$ $74.740$ 3.3.1849.1 None \(0\) \(0\) \(3\) \(-5\) $+$ $-$ $-$ $-$ $\mathrm{SU}(2)$ \(q+q^{5}+(-2+\beta _{1})q^{7}+(1+\beta _{2})q^{11}+\cdots\)
9360.2.a.dc 9360.a 1.a $3$ $74.740$ 3.3.621.1 None \(0\) \(0\) \(3\) \(-3\) $+$ $+$ $-$ $-$ $\mathrm{SU}(2)$ \(q+q^{5}+(-1-\beta _{2})q^{7}+(-1+\beta _{1}+\beta _{2})q^{11}+\cdots\)
9360.2.a.dd 9360.a 1.a $3$ $74.740$ 3.3.316.1 None \(0\) \(0\) \(3\) \(-1\) $-$ $-$ $-$ $-$ $\mathrm{SU}(2)$ \(q+q^{5}+\beta _{1}q^{7}-\beta _{1}q^{11}+q^{13}+(-\beta _{1}+\cdots)q^{17}+\cdots\)
9360.2.a.de 9360.a 1.a $3$ $74.740$ 3.3.1016.1 None \(0\) \(0\) \(3\) \(1\) $+$ $+$ $-$ $+$ $\mathrm{SU}(2)$ \(q+q^{5}+\beta _{2}q^{7}+(2-\beta _{1})q^{11}-q^{13}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_0(9360))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_0(9360)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_0(15))\)\(^{\oplus 20}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(20))\)\(^{\oplus 18}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(24))\)\(^{\oplus 16}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(26))\)\(^{\oplus 24}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(30))\)\(^{\oplus 16}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(36))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(39))\)\(^{\oplus 20}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(40))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(45))\)\(^{\oplus 10}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(48))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(52))\)\(^{\oplus 18}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(65))\)\(^{\oplus 15}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(72))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(78))\)\(^{\oplus 16}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(80))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(90))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(104))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(117))\)\(^{\oplus 10}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(120))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(130))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(144))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(156))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(180))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(195))\)\(^{\oplus 10}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(208))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(234))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(240))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(260))\)\(^{\oplus 9}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(312))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(360))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(390))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(468))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(520))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(585))\)\(^{\oplus 5}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(624))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(720))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(780))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(936))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(1040))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(1170))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(1560))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(1872))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(2340))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(3120))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(4680))\)\(^{\oplus 2}\)