Properties

Label 9576.2.a
Level $9576$
Weight $2$
Character orbit 9576.a
Rep. character $\chi_{9576}(1,\cdot)$
Character field $\Q$
Dimension $134$
Newform subspaces $67$
Sturm bound $3840$
Trace bound $17$

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Defining parameters

Level: \( N \) \(=\) \( 9576 = 2^{3} \cdot 3^{2} \cdot 7 \cdot 19 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 9576.a (trivial)
Character field: \(\Q\)
Newform subspaces: \( 67 \)
Sturm bound: \(3840\)
Trace bound: \(17\)
Distinguishing \(T_p\): \(5\), \(11\), \(13\), \(17\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_0(9576))\).

Total New Old
Modular forms 1952 134 1818
Cusp forms 1889 134 1755
Eisenstein series 63 0 63

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

\(2\)\(3\)\(7\)\(19\)FrickeDim.
\(+\)\(+\)\(+\)\(+\)\(+\)\(6\)
\(+\)\(+\)\(+\)\(-\)\(-\)\(7\)
\(+\)\(+\)\(-\)\(+\)\(-\)\(7\)
\(+\)\(+\)\(-\)\(-\)\(+\)\(6\)
\(+\)\(-\)\(+\)\(+\)\(-\)\(12\)
\(+\)\(-\)\(+\)\(-\)\(+\)\(9\)
\(+\)\(-\)\(-\)\(+\)\(+\)\(9\)
\(+\)\(-\)\(-\)\(-\)\(-\)\(12\)
\(-\)\(+\)\(+\)\(+\)\(-\)\(6\)
\(-\)\(+\)\(+\)\(-\)\(+\)\(7\)
\(-\)\(+\)\(-\)\(+\)\(+\)\(7\)
\(-\)\(+\)\(-\)\(-\)\(-\)\(6\)
\(-\)\(-\)\(+\)\(+\)\(+\)\(9\)
\(-\)\(-\)\(+\)\(-\)\(-\)\(11\)
\(-\)\(-\)\(-\)\(+\)\(-\)\(11\)
\(-\)\(-\)\(-\)\(-\)\(+\)\(9\)
Plus space\(+\)\(62\)
Minus space\(-\)\(72\)

Trace form

\( 134 q + 4 q^{5} + O(q^{10}) \) \( 134 q + 4 q^{5} - 12 q^{11} + 4 q^{13} + 4 q^{17} + 134 q^{25} - 4 q^{29} + 16 q^{31} - 12 q^{35} + 4 q^{37} - 4 q^{41} + 20 q^{43} + 134 q^{49} - 20 q^{53} + 16 q^{55} + 16 q^{59} + 4 q^{61} + 8 q^{65} - 24 q^{71} + 12 q^{73} + 8 q^{77} + 40 q^{79} + 32 q^{83} - 24 q^{85} - 20 q^{89} + 8 q^{91} - 4 q^{97} + O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(9576))\) 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 7 19
9576.2.a.a 9576.a 1.a $1$ $76.465$ \(\Q\) None \(0\) \(0\) \(-4\) \(-1\) $-$ $+$ $+$ $-$ $\mathrm{SU}(2)$ \(q-4q^{5}-q^{7}+2q^{11}+2q^{13}+q^{19}+\cdots\)
9576.2.a.b 9576.a 1.a $1$ $76.465$ \(\Q\) None \(0\) \(0\) \(-2\) \(-1\) $+$ $-$ $+$ $-$ $\mathrm{SU}(2)$ \(q-2q^{5}-q^{7}-6q^{11}-2q^{13}+8q^{17}+\cdots\)
9576.2.a.c 9576.a 1.a $1$ $76.465$ \(\Q\) None \(0\) \(0\) \(-2\) \(-1\) $-$ $-$ $+$ $-$ $\mathrm{SU}(2)$ \(q-2q^{5}-q^{7}-4q^{11}-6q^{13}-6q^{17}+\cdots\)
9576.2.a.d 9576.a 1.a $1$ $76.465$ \(\Q\) None \(0\) \(0\) \(-2\) \(-1\) $+$ $+$ $+$ $+$ $\mathrm{SU}(2)$ \(q-2q^{5}-q^{7}+2q^{11}-4q^{13}+4q^{17}+\cdots\)
9576.2.a.e 9576.a 1.a $1$ $76.465$ \(\Q\) None \(0\) \(0\) \(-2\) \(-1\) $+$ $-$ $+$ $+$ $\mathrm{SU}(2)$ \(q-2q^{5}-q^{7}+4q^{11}-6q^{13}-2q^{17}+\cdots\)
9576.2.a.f 9576.a 1.a $1$ $76.465$ \(\Q\) None \(0\) \(0\) \(-2\) \(-1\) $-$ $-$ $+$ $-$ $\mathrm{SU}(2)$ \(q-2q^{5}-q^{7}+6q^{11}-2q^{13}+q^{19}+\cdots\)
9576.2.a.g 9576.a 1.a $1$ $76.465$ \(\Q\) None \(0\) \(0\) \(-2\) \(1\) $+$ $+$ $-$ $-$ $\mathrm{SU}(2)$ \(q-2q^{5}+q^{7}-2q^{11}+2q^{13}+2q^{17}+\cdots\)
9576.2.a.h 9576.a 1.a $1$ $76.465$ \(\Q\) None \(0\) \(0\) \(-2\) \(1\) $-$ $+$ $-$ $+$ $\mathrm{SU}(2)$ \(q-2q^{5}+q^{7}+6q^{11}-4q^{17}-q^{19}+\cdots\)
9576.2.a.i 9576.a 1.a $1$ $76.465$ \(\Q\) None \(0\) \(0\) \(0\) \(-1\) $-$ $-$ $+$ $+$ $\mathrm{SU}(2)$ \(q-q^{7}-6q^{11}+4q^{13}-q^{19}+2q^{23}+\cdots\)
9576.2.a.j 9576.a 1.a $1$ $76.465$ \(\Q\) None \(0\) \(0\) \(0\) \(-1\) $+$ $-$ $+$ $-$ $\mathrm{SU}(2)$ \(q-q^{7}-2q^{13}+q^{19}-4q^{23}-5q^{25}+\cdots\)
9576.2.a.k 9576.a 1.a $1$ $76.465$ \(\Q\) None \(0\) \(0\) \(0\) \(1\) $-$ $+$ $-$ $-$ $\mathrm{SU}(2)$ \(q+q^{7}-4q^{11}+2q^{13}+2q^{17}+q^{19}+\cdots\)
9576.2.a.l 9576.a 1.a $1$ $76.465$ \(\Q\) None \(0\) \(0\) \(0\) \(1\) $-$ $-$ $-$ $-$ $\mathrm{SU}(2)$ \(q+q^{7}-2q^{11}-4q^{13}+q^{19}+6q^{23}+\cdots\)
9576.2.a.m 9576.a 1.a $1$ $76.465$ \(\Q\) None \(0\) \(0\) \(0\) \(1\) $-$ $+$ $-$ $+$ $\mathrm{SU}(2)$ \(q+q^{7}-2q^{11}+6q^{13}-q^{19}-6q^{23}+\cdots\)
9576.2.a.n 9576.a 1.a $1$ $76.465$ \(\Q\) None \(0\) \(0\) \(0\) \(1\) $-$ $-$ $-$ $+$ $\mathrm{SU}(2)$ \(q+q^{7}-2q^{13}+8q^{17}-q^{19}+4q^{23}+\cdots\)
9576.2.a.o 9576.a 1.a $1$ $76.465$ \(\Q\) None \(0\) \(0\) \(0\) \(1\) $+$ $+$ $-$ $+$ $\mathrm{SU}(2)$ \(q+q^{7}+2q^{11}+6q^{13}-q^{19}+6q^{23}+\cdots\)
9576.2.a.p 9576.a 1.a $1$ $76.465$ \(\Q\) None \(0\) \(0\) \(0\) \(1\) $+$ $+$ $-$ $-$ $\mathrm{SU}(2)$ \(q+q^{7}+4q^{11}+2q^{13}-2q^{17}+q^{19}+\cdots\)
9576.2.a.q 9576.a 1.a $1$ $76.465$ \(\Q\) None \(0\) \(0\) \(0\) \(1\) $-$ $-$ $-$ $-$ $\mathrm{SU}(2)$ \(q+q^{7}+4q^{11}+2q^{13}+q^{19}-5q^{25}+\cdots\)
9576.2.a.r 9576.a 1.a $1$ $76.465$ \(\Q\) None \(0\) \(0\) \(2\) \(-1\) $-$ $+$ $+$ $+$ $\mathrm{SU}(2)$ \(q+2q^{5}-q^{7}-2q^{11}-4q^{13}-4q^{17}+\cdots\)
9576.2.a.s 9576.a 1.a $1$ $76.465$ \(\Q\) None \(0\) \(0\) \(2\) \(-1\) $-$ $-$ $+$ $-$ $\mathrm{SU}(2)$ \(q+2q^{5}-q^{7}-2q^{13}-2q^{17}+q^{19}+\cdots\)
9576.2.a.t 9576.a 1.a $1$ $76.465$ \(\Q\) None \(0\) \(0\) \(2\) \(-1\) $-$ $-$ $+$ $-$ $\mathrm{SU}(2)$ \(q+2q^{5}-q^{7}+4q^{11}+2q^{13}+6q^{17}+\cdots\)
9576.2.a.u 9576.a 1.a $1$ $76.465$ \(\Q\) None \(0\) \(0\) \(2\) \(1\) $+$ $+$ $-$ $+$ $\mathrm{SU}(2)$ \(q+2q^{5}+q^{7}-6q^{11}+4q^{17}-q^{19}+\cdots\)
9576.2.a.v 9576.a 1.a $1$ $76.465$ \(\Q\) None \(0\) \(0\) \(2\) \(1\) $+$ $-$ $-$ $+$ $\mathrm{SU}(2)$ \(q+2q^{5}+q^{7}-2q^{13}-6q^{17}-q^{19}+\cdots\)
9576.2.a.w 9576.a 1.a $1$ $76.465$ \(\Q\) None \(0\) \(0\) \(2\) \(1\) $-$ $+$ $-$ $-$ $\mathrm{SU}(2)$ \(q+2q^{5}+q^{7}+2q^{11}+2q^{13}-2q^{17}+\cdots\)
9576.2.a.x 9576.a 1.a $1$ $76.465$ \(\Q\) None \(0\) \(0\) \(2\) \(1\) $-$ $-$ $-$ $+$ $\mathrm{SU}(2)$ \(q+2q^{5}+q^{7}+4q^{11}+2q^{13}-2q^{17}+\cdots\)
9576.2.a.y 9576.a 1.a $1$ $76.465$ \(\Q\) None \(0\) \(0\) \(4\) \(-1\) $+$ $-$ $+$ $+$ $\mathrm{SU}(2)$ \(q+4q^{5}-q^{7}-4q^{11}+2q^{13}+4q^{17}+\cdots\)
9576.2.a.z 9576.a 1.a $1$ $76.465$ \(\Q\) None \(0\) \(0\) \(4\) \(-1\) $+$ $+$ $+$ $-$ $\mathrm{SU}(2)$ \(q+4q^{5}-q^{7}-2q^{11}+2q^{13}+q^{19}+\cdots\)
9576.2.a.ba 9576.a 1.a $1$ $76.465$ \(\Q\) None \(0\) \(0\) \(4\) \(-1\) $+$ $-$ $+$ $-$ $\mathrm{SU}(2)$ \(q+4q^{5}-q^{7}-2q^{13}-4q^{17}+q^{19}+\cdots\)
9576.2.a.bb 9576.a 1.a $1$ $76.465$ \(\Q\) None \(0\) \(0\) \(4\) \(1\) $+$ $-$ $-$ $-$ $\mathrm{SU}(2)$ \(q+4q^{5}+q^{7}-2q^{11}-4q^{13}-4q^{17}+\cdots\)
9576.2.a.bc 9576.a 1.a $2$ $76.465$ \(\Q(\sqrt{5}) \) None \(0\) \(0\) \(-5\) \(2\) $-$ $-$ $-$ $+$ $\mathrm{SU}(2)$ \(q+(-2-\beta )q^{5}+q^{7}+(1+3\beta )q^{11}+\cdots\)
9576.2.a.bd 9576.a 1.a $2$ $76.465$ \(\Q(\sqrt{17}) \) None \(0\) \(0\) \(-4\) \(-2\) $-$ $+$ $+$ $+$ $\mathrm{SU}(2)$ \(q-2q^{5}-q^{7}+2q^{11}+(1+\beta )q^{13}+\cdots\)
9576.2.a.be 9576.a 1.a $2$ $76.465$ \(\Q(\sqrt{5}) \) None \(0\) \(0\) \(-2\) \(-2\) $+$ $+$ $+$ $-$ $\mathrm{SU}(2)$ \(q+(-1-\beta )q^{5}-q^{7}+2\beta q^{11}+2\beta q^{13}+\cdots\)
9576.2.a.bf 9576.a 1.a $2$ $76.465$ \(\Q(\sqrt{3}) \) None \(0\) \(0\) \(-2\) \(-2\) $-$ $+$ $+$ $-$ $\mathrm{SU}(2)$ \(q+(-1+\beta )q^{5}-q^{7}+2\beta q^{11}+4q^{13}+\cdots\)
9576.2.a.bg 9576.a 1.a $2$ $76.465$ \(\Q(\sqrt{5}) \) None \(0\) \(0\) \(-2\) \(-2\) $+$ $+$ $+$ $-$ $\mathrm{SU}(2)$ \(q+(-1-\beta )q^{5}-q^{7}+(3-\beta )q^{11}+(-3+\cdots)q^{13}+\cdots\)
9576.2.a.bh 9576.a 1.a $2$ $76.465$ \(\Q(\sqrt{7}) \) None \(0\) \(0\) \(-2\) \(2\) $+$ $+$ $-$ $-$ $\mathrm{SU}(2)$ \(q+(-1+\beta )q^{5}+q^{7}-2q^{11}-4q^{13}+\cdots\)
9576.2.a.bi 9576.a 1.a $2$ $76.465$ \(\Q(\sqrt{5}) \) None \(0\) \(0\) \(-2\) \(2\) $-$ $+$ $-$ $+$ $\mathrm{SU}(2)$ \(q+(-1-\beta )q^{5}+q^{7}-2q^{11}+2\beta q^{13}+\cdots\)
9576.2.a.bj 9576.a 1.a $2$ $76.465$ \(\Q(\sqrt{3}) \) None \(0\) \(0\) \(-2\) \(2\) $+$ $-$ $-$ $+$ $\mathrm{SU}(2)$ \(q+(-1+\beta )q^{5}+q^{7}+(-2+2\beta )q^{13}+\cdots\)
9576.2.a.bk 9576.a 1.a $2$ $76.465$ \(\Q(\sqrt{3}) \) None \(0\) \(0\) \(0\) \(-2\) $-$ $-$ $+$ $+$ $\mathrm{SU}(2)$ \(q+\beta q^{5}-q^{7}-2q^{13}-\beta q^{17}-q^{19}+\cdots\)
9576.2.a.bl 9576.a 1.a $2$ $76.465$ \(\Q(\sqrt{2}) \) None \(0\) \(0\) \(0\) \(2\) $+$ $+$ $-$ $-$ $\mathrm{SU}(2)$ \(q+\beta q^{5}+q^{7}-2q^{11}+(2-\beta )q^{13}+\cdots\)
9576.2.a.bm 9576.a 1.a $2$ $76.465$ \(\Q(\sqrt{5}) \) None \(0\) \(0\) \(0\) \(2\) $-$ $-$ $-$ $-$ $\mathrm{SU}(2)$ \(q+(1-2\beta )q^{5}+q^{7}+(-1+3\beta )q^{11}+\cdots\)
9576.2.a.bn 9576.a 1.a $2$ $76.465$ \(\Q(\sqrt{5}) \) None \(0\) \(0\) \(0\) \(2\) $+$ $-$ $-$ $+$ $\mathrm{SU}(2)$ \(q+(1-2\beta )q^{5}+q^{7}+(-1+3\beta )q^{11}+\cdots\)
9576.2.a.bo 9576.a 1.a $2$ $76.465$ \(\Q(\sqrt{2}) \) None \(0\) \(0\) \(0\) \(2\) $-$ $+$ $-$ $-$ $\mathrm{SU}(2)$ \(q+\beta q^{5}+q^{7}+2q^{11}+(2+\beta )q^{13}+\cdots\)
9576.2.a.bp 9576.a 1.a $2$ $76.465$ \(\Q(\sqrt{5}) \) None \(0\) \(0\) \(2\) \(-2\) $-$ $+$ $+$ $-$ $\mathrm{SU}(2)$ \(q+(1+\beta )q^{5}-q^{7}+(-3+\beta )q^{11}+(-3+\cdots)q^{13}+\cdots\)
9576.2.a.bq 9576.a 1.a $2$ $76.465$ \(\Q(\sqrt{5}) \) None \(0\) \(0\) \(2\) \(-2\) $-$ $+$ $+$ $-$ $\mathrm{SU}(2)$ \(q+(1+\beta )q^{5}-q^{7}-2\beta q^{11}+2\beta q^{13}+\cdots\)
9576.2.a.br 9576.a 1.a $2$ $76.465$ \(\Q(\sqrt{3}) \) None \(0\) \(0\) \(2\) \(-2\) $+$ $+$ $+$ $-$ $\mathrm{SU}(2)$ \(q+(1+\beta )q^{5}-q^{7}+2\beta q^{11}+4q^{13}+\cdots\)
9576.2.a.bs 9576.a 1.a $2$ $76.465$ \(\Q(\sqrt{13}) \) None \(0\) \(0\) \(2\) \(-2\) $+$ $-$ $+$ $-$ $\mathrm{SU}(2)$ \(q+q^{5}-q^{7}+\beta q^{11}+(1-2\beta )q^{13}+\cdots\)
9576.2.a.bt 9576.a 1.a $2$ $76.465$ \(\Q(\sqrt{5}) \) None \(0\) \(0\) \(2\) \(-2\) $-$ $-$ $+$ $+$ $\mathrm{SU}(2)$ \(q+q^{5}-q^{7}+(-1+3\beta )q^{11}+(3-4\beta )q^{13}+\cdots\)
9576.2.a.bu 9576.a 1.a $2$ $76.465$ \(\Q(\sqrt{7}) \) None \(0\) \(0\) \(2\) \(2\) $-$ $+$ $-$ $-$ $\mathrm{SU}(2)$ \(q+(1+\beta )q^{5}+q^{7}+2q^{11}-4q^{13}+\cdots\)
9576.2.a.bv 9576.a 1.a $2$ $76.465$ \(\Q(\sqrt{5}) \) None \(0\) \(0\) \(2\) \(2\) $+$ $+$ $-$ $+$ $\mathrm{SU}(2)$ \(q+(1+\beta )q^{5}+q^{7}+2q^{11}+2\beta q^{13}+\cdots\)
9576.2.a.bw 9576.a 1.a $2$ $76.465$ \(\Q(\sqrt{3}) \) None \(0\) \(0\) \(2\) \(2\) $+$ $-$ $-$ $-$ $\mathrm{SU}(2)$ \(q+(1+\beta )q^{5}+q^{7}+4q^{11}+(2+2\beta )q^{13}+\cdots\)
9576.2.a.bx 9576.a 1.a $2$ $76.465$ \(\Q(\sqrt{17}) \) None \(0\) \(0\) \(4\) \(-2\) $+$ $+$ $+$ $+$ $\mathrm{SU}(2)$ \(q+2q^{5}-q^{7}-2q^{11}+(1+\beta )q^{13}+\cdots\)
9576.2.a.by 9576.a 1.a $2$ $76.465$ \(\Q(\sqrt{2}) \) None \(0\) \(0\) \(4\) \(-2\) $-$ $-$ $+$ $-$ $\mathrm{SU}(2)$ \(q+(2+\beta )q^{5}-q^{7}+2\beta q^{11}+4\beta q^{13}+\cdots\)
9576.2.a.bz 9576.a 1.a $3$ $76.465$ 3.3.316.1 None \(0\) \(0\) \(-4\) \(-3\) $+$ $+$ $+$ $+$ $\mathrm{SU}(2)$ \(q+(-1+\beta _{2})q^{5}-q^{7}+2\beta _{2}q^{11}+(1+\cdots)q^{17}+\cdots\)
9576.2.a.ca 9576.a 1.a $3$ $76.465$ 3.3.1101.1 None \(0\) \(0\) \(-2\) \(3\) $-$ $-$ $-$ $+$ $\mathrm{SU}(2)$ \(q+(-1-\beta _{2})q^{5}+q^{7}+(-3+\beta _{1}-\beta _{2})q^{11}+\cdots\)
9576.2.a.cb 9576.a 1.a $3$ $76.465$ 3.3.568.1 None \(0\) \(0\) \(0\) \(-3\) $+$ $-$ $+$ $+$ $\mathrm{SU}(2)$ \(q+\beta _{1}q^{5}-q^{7}+(1+\beta _{1}+\beta _{2})q^{11}+\cdots\)
9576.2.a.cc 9576.a 1.a $3$ $76.465$ 3.3.316.1 None \(0\) \(0\) \(0\) \(-3\) $+$ $-$ $+$ $+$ $\mathrm{SU}(2)$ \(q-q^{7}+(1-\beta _{1})q^{11}+(-2-\beta _{2})q^{13}+\cdots\)
9576.2.a.cd 9576.a 1.a $3$ $76.465$ 3.3.1772.1 None \(0\) \(0\) \(0\) \(3\) $-$ $+$ $-$ $+$ $\mathrm{SU}(2)$ \(q+\beta _{2}q^{5}+q^{7}-2q^{11}+(-3+\beta _{1}+\cdots)q^{17}+\cdots\)
9576.2.a.ce 9576.a 1.a $3$ $76.465$ 3.3.1772.1 None \(0\) \(0\) \(0\) \(3\) $+$ $+$ $-$ $+$ $\mathrm{SU}(2)$ \(q-\beta _{2}q^{5}+q^{7}+2q^{11}+(3-\beta _{1})q^{17}+\cdots\)
9576.2.a.cf 9576.a 1.a $3$ $76.465$ 3.3.316.1 None \(0\) \(0\) \(4\) \(-3\) $-$ $+$ $+$ $+$ $\mathrm{SU}(2)$ \(q+(1-\beta _{2})q^{5}-q^{7}-2\beta _{2}q^{11}+(-1+\cdots)q^{17}+\cdots\)
9576.2.a.cg 9576.a 1.a $4$ $76.465$ 4.4.7232.1 None \(0\) \(0\) \(-4\) \(-4\) $+$ $-$ $+$ $-$ $\mathrm{SU}(2)$ \(q+(-1+\beta _{1})q^{5}-q^{7}+\beta _{2}q^{11}+(1+\cdots)q^{13}+\cdots\)
9576.2.a.ch 9576.a 1.a $4$ $76.465$ 4.4.2225.1 None \(0\) \(0\) \(-4\) \(4\) $+$ $-$ $-$ $+$ $\mathrm{SU}(2)$ \(q+(-1+\beta _{2})q^{5}+q^{7}+(-1+\beta _{3})q^{11}+\cdots\)
9576.2.a.ci 9576.a 1.a $4$ $76.465$ 4.4.25857.1 None \(0\) \(0\) \(-1\) \(4\) $+$ $-$ $-$ $-$ $\mathrm{SU}(2)$ \(q-\beta _{1}q^{5}+q^{7}+(-\beta _{1}+\beta _{2}+\beta _{3})q^{11}+\cdots\)
9576.2.a.cj 9576.a 1.a $4$ $76.465$ 4.4.9248.1 None \(0\) \(0\) \(0\) \(-4\) $-$ $-$ $+$ $+$ $\mathrm{SU}(2)$ \(q+\beta _{1}q^{5}-q^{7}+(-\beta _{1}+\beta _{2})q^{11}+(1+\cdots)q^{17}+\cdots\)
9576.2.a.ck 9576.a 1.a $4$ $76.465$ 4.4.18097.1 None \(0\) \(0\) \(3\) \(-4\) $+$ $-$ $+$ $+$ $\mathrm{SU}(2)$ \(q+(1+\beta _{2}-\beta _{3})q^{5}-q^{7}+(-1-\beta _{1}+\cdots)q^{11}+\cdots\)
9576.2.a.cl 9576.a 1.a $4$ $76.465$ 4.4.13068.1 None \(0\) \(0\) \(4\) \(4\) $-$ $-$ $-$ $+$ $\mathrm{SU}(2)$ \(q+(1-\beta _{2})q^{5}+q^{7}+(-\beta _{1}-\beta _{3})q^{11}+\cdots\)
9576.2.a.cm 9576.a 1.a $5$ $76.465$ 5.5.10463409.1 None \(0\) \(0\) \(-3\) \(-5\) $-$ $-$ $+$ $-$ $\mathrm{SU}(2)$ \(q+(-1+\beta _{4})q^{5}-q^{7}+(-1+\beta _{1}-\beta _{3}+\cdots)q^{11}+\cdots\)
9576.2.a.cn 9576.a 1.a $5$ $76.465$ 5.5.401584.1 None \(0\) \(0\) \(-2\) \(5\) $-$ $-$ $-$ $-$ $\mathrm{SU}(2)$ \(q+\beta _{1}q^{5}+q^{7}+(-1+\beta _{2}-\beta _{3})q^{11}+\cdots\)
9576.2.a.co 9576.a 1.a $5$ $76.465$ 5.5.135076.1 None \(0\) \(0\) \(-2\) \(5\) $+$ $-$ $-$ $-$ $\mathrm{SU}(2)$ \(q-\beta _{1}q^{5}+q^{7}+\beta _{4}q^{11}+(2-\beta _{3})q^{13}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_0(9576))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_0(9576)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_0(14))\)\(^{\oplus 18}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(19))\)\(^{\oplus 24}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(21))\)\(^{\oplus 16}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(24))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(36))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(38))\)\(^{\oplus 18}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(42))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(56))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(57))\)\(^{\oplus 16}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(63))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(72))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(76))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(84))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(114))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(126))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(133))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(152))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(168))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(171))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(228))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(252))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(266))\)\(^{\oplus 9}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(342))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(399))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(456))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(504))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(532))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(684))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(798))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(1064))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(1197))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(1368))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(1596))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(2394))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(3192))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(4788))\)\(^{\oplus 2}\)