Properties

Label 2312.4.a
Level $2312$
Weight $4$
Character orbit 2312.a
Rep. character $\chi_{2312}(1,\cdot)$
Character field $\Q$
Dimension $203$
Newform subspaces $19$
Sturm bound $1224$
Trace bound $9$

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Defining parameters

Level: \( N \) \(=\) \( 2312 = 2^{3} \cdot 17^{2} \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 2312.a (trivial)
Character field: \(\Q\)
Newform subspaces: \( 19 \)
Sturm bound: \(1224\)
Trace bound: \(9\)
Distinguishing \(T_p\): \(3\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{4}(\Gamma_0(2312))\).

Total New Old
Modular forms 954 203 751
Cusp forms 882 203 679
Eisenstein series 72 0 72

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

\(2\)\(17\)FrickeDim.
\(+\)\(+\)\(+\)\(53\)
\(+\)\(-\)\(-\)\(48\)
\(-\)\(+\)\(-\)\(50\)
\(-\)\(-\)\(+\)\(52\)
Plus space\(+\)\(105\)
Minus space\(-\)\(98\)

Trace form

\( 203 q - 2 q^{3} + 12 q^{5} + 24 q^{7} + 1819 q^{9} + O(q^{10}) \) \( 203 q - 2 q^{3} + 12 q^{5} + 24 q^{7} + 1819 q^{9} + 6 q^{11} - 58 q^{13} + 8 q^{15} + 68 q^{19} - 220 q^{21} + 28 q^{23} + 4969 q^{25} + 76 q^{27} + 60 q^{29} - 376 q^{31} + 64 q^{33} - 212 q^{35} + 488 q^{37} + 20 q^{39} - 230 q^{41} + 284 q^{43} + 652 q^{45} + 768 q^{47} + 10435 q^{49} - 6 q^{53} + 316 q^{55} - 1064 q^{57} + 340 q^{59} + 680 q^{61} + 1872 q^{63} - 72 q^{65} + 692 q^{67} + 1772 q^{69} - 900 q^{71} + 1510 q^{73} + 2058 q^{75} + 628 q^{77} - 844 q^{79} + 15883 q^{81} + 1268 q^{83} + 44 q^{87} - 886 q^{89} + 1512 q^{91} - 844 q^{93} - 4448 q^{95} - 1150 q^{97} - 1026 q^{99} + O(q^{100}) \)

Decomposition of \(S_{4}^{\mathrm{new}}(\Gamma_0(2312))\) 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 17
2312.4.a.a 2312.a 1.a $1$ $136.412$ \(\Q\) None \(0\) \(4\) \(2\) \(-24\) $+$ $+$ $\mathrm{SU}(2)$ \(q+4q^{3}+2q^{5}-24q^{7}-11q^{9}+44q^{11}+\cdots\)
2312.4.a.b 2312.a 1.a $2$ $136.412$ \(\Q(\sqrt{3}) \) None \(0\) \(-4\) \(12\) \(36\) $+$ $+$ $\mathrm{SU}(2)$ \(q+(-2+\beta )q^{3}+(6-2\beta )q^{5}+(18-3\beta )q^{7}+\cdots\)
2312.4.a.c 2312.a 1.a $3$ $136.412$ 3.3.1556.1 None \(0\) \(-8\) \(-2\) \(-12\) $-$ $+$ $\mathrm{SU}(2)$ \(q+(-3+\beta _{2})q^{3}+(-1+\beta _{1})q^{5}+(-4+\cdots)q^{7}+\cdots\)
2312.4.a.d 2312.a 1.a $3$ $136.412$ 3.3.8396.1 None \(0\) \(4\) \(8\) \(2\) $-$ $+$ $\mathrm{SU}(2)$ \(q+(1-\beta _{2})q^{3}+(3-\beta _{1}+2\beta _{2})q^{5}+(2+\cdots)q^{7}+\cdots\)
2312.4.a.e 2312.a 1.a $4$ $136.412$ 4.4.550476.1 None \(0\) \(2\) \(-8\) \(22\) $+$ $+$ $\mathrm{SU}(2)$ \(q+\beta _{1}q^{3}+(-1+\beta _{1}+\beta _{2}+2\beta _{3})q^{5}+\cdots\)
2312.4.a.f 2312.a 1.a $6$ $136.412$ \(\mathbb{Q}[x]/(x^{6} - \cdots)\) None \(0\) \(-7\) \(-3\) \(-7\) $-$ $+$ $\mathrm{SU}(2)$ \(q+(-1-\beta _{1})q^{3}+(-1+\beta _{2})q^{5}+(-1+\cdots)q^{7}+\cdots\)
2312.4.a.g 2312.a 1.a $6$ $136.412$ \(\mathbb{Q}[x]/(x^{6} - \cdots)\) None \(0\) \(-1\) \(-13\) \(-1\) $+$ $-$ $\mathrm{SU}(2)$ \(q+\beta _{3}q^{3}+(-2+\beta _{2})q^{5}+\beta _{1}q^{7}+(10+\cdots)q^{9}+\cdots\)
2312.4.a.h 2312.a 1.a $6$ $136.412$ \(\mathbb{Q}[x]/(x^{6} - \cdots)\) None \(0\) \(0\) \(0\) \(0\) $-$ $+$ $\mathrm{SU}(2)$ \(q+\beta _{1}q^{3}+\beta _{4}q^{5}+(-\beta _{1}+\beta _{2}+\beta _{4}+\cdots)q^{7}+\cdots\)
2312.4.a.i 2312.a 1.a $6$ $136.412$ \(\mathbb{Q}[x]/(x^{6} - \cdots)\) None \(0\) \(1\) \(13\) \(1\) $+$ $+$ $\mathrm{SU}(2)$ \(q-\beta _{3}q^{3}+(2-\beta _{2})q^{5}-\beta _{1}q^{7}+(10+\cdots)q^{9}+\cdots\)
2312.4.a.j 2312.a 1.a $6$ $136.412$ \(\mathbb{Q}[x]/(x^{6} - \cdots)\) None \(0\) \(7\) \(3\) \(7\) $-$ $-$ $\mathrm{SU}(2)$ \(q+(1+\beta _{1})q^{3}+(1-\beta _{2})q^{5}+(1+\beta _{5})q^{7}+\cdots\)
2312.4.a.k 2312.a 1.a $8$ $136.412$ \(\mathbb{Q}[x]/(x^{8} - \cdots)\) None \(0\) \(0\) \(0\) \(0\) $+$ $+$ $\mathrm{SU}(2)$ \(q-\beta _{2}q^{3}+\beta _{4}q^{5}+(-\beta _{1}-\beta _{2}-\beta _{4}+\cdots)q^{7}+\cdots\)
2312.4.a.l 2312.a 1.a $14$ $136.412$ \(\mathbb{Q}[x]/(x^{14} - \cdots)\) None \(0\) \(0\) \(0\) \(0\) $+$ $+$ $\mathrm{SU}(2)$ \(q+\beta _{3}q^{3}+\beta _{8}q^{5}+(-\beta _{1}+\beta _{4})q^{7}+\cdots\)
2312.4.a.m 2312.a 1.a $14$ $136.412$ \(\mathbb{Q}[x]/(x^{14} - \cdots)\) None \(0\) \(0\) \(0\) \(0\) $-$ $+$ $\mathrm{SU}(2)$ \(q+\beta _{3}q^{3}+(-\beta _{1}+\beta _{9})q^{5}+(\beta _{1}+\beta _{5}+\cdots)q^{7}+\cdots\)
2312.4.a.n 2312.a 1.a $18$ $136.412$ \(\mathbb{Q}[x]/(x^{18} - \cdots)\) None \(0\) \(-18\) \(0\) \(-51\) $-$ $+$ $\mathrm{SU}(2)$ \(q+(-1+\beta _{1})q^{3}-\beta _{5}q^{5}+(-3-\beta _{4}+\cdots)q^{7}+\cdots\)
2312.4.a.o 2312.a 1.a $18$ $136.412$ \(\mathbb{Q}[x]/(x^{18} - \cdots)\) None \(0\) \(0\) \(-30\) \(-33\) $+$ $-$ $\mathrm{SU}(2)$ \(q+\beta _{1}q^{3}+(-2-\beta _{11})q^{5}+(-2-\beta _{1}+\cdots)q^{7}+\cdots\)
2312.4.a.p 2312.a 1.a $18$ $136.412$ \(\mathbb{Q}[x]/(x^{18} - \cdots)\) None \(0\) \(0\) \(30\) \(33\) $+$ $+$ $\mathrm{SU}(2)$ \(q-\beta _{1}q^{3}+(2+\beta _{11})q^{5}+(2+\beta _{1}+\beta _{12}+\cdots)q^{7}+\cdots\)
2312.4.a.q 2312.a 1.a $18$ $136.412$ \(\mathbb{Q}[x]/(x^{18} - \cdots)\) None \(0\) \(18\) \(0\) \(51\) $-$ $-$ $\mathrm{SU}(2)$ \(q+(1-\beta _{1})q^{3}+\beta _{5}q^{5}+(3+\beta _{4}-\beta _{10}+\cdots)q^{7}+\cdots\)
2312.4.a.r 2312.a 1.a $24$ $136.412$ None \(0\) \(0\) \(0\) \(0\) $+$ $-$ $\mathrm{SU}(2)$
2312.4.a.s 2312.a 1.a $28$ $136.412$ None \(0\) \(0\) \(0\) \(0\) $-$ $-$ $\mathrm{SU}(2)$

Decomposition of \(S_{4}^{\mathrm{old}}(\Gamma_0(2312))\) into lower level spaces

\( S_{4}^{\mathrm{old}}(\Gamma_0(2312)) \cong \) \(S_{4}^{\mathrm{new}}(\Gamma_0(8))\)\(^{\oplus 3}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_0(17))\)\(^{\oplus 8}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_0(34))\)\(^{\oplus 6}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_0(68))\)\(^{\oplus 4}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_0(136))\)\(^{\oplus 2}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_0(289))\)\(^{\oplus 4}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_0(578))\)\(^{\oplus 3}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_0(1156))\)\(^{\oplus 2}\)