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Properties

Label 576.3.m
Level $576$
Weight $3$
Character orbit 576.m
Rep. character $\chi_{576}(271,\cdot)$
Character field $\Q(\zeta_{4})$
Dimension $38$
Newform subspaces $3$
Sturm bound $288$
Trace bound $11$

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Defining parameters

Level: \( N \) \(=\) \( 576 = 2^{6} \cdot 3^{2} \)
Weight: \( k \) \(=\) \( 3 \)
Character orbit: \([\chi]\) \(=\) 576.m (of order \(4\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 16 \)
Character field: \(\Q(i)\)
Newform subspaces: \( 3 \)
Sturm bound: \(288\)
Trace bound: \(11\)
Distinguishing \(T_p\): \(5\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{3}(576, [\chi])\).

Total New Old
Modular forms 416 42 374
Cusp forms 352 38 314
Eisenstein series 64 4 60

Trace form

\( 38 q + 2 q^{5} + 4 q^{7} + O(q^{10}) \) \( 38 q + 2 q^{5} + 4 q^{7} + 14 q^{11} - 2 q^{13} + 4 q^{17} + 34 q^{19} - 68 q^{23} - 14 q^{29} - 4 q^{35} + 46 q^{37} - 14 q^{43} + 178 q^{49} + 82 q^{53} + 260 q^{55} + 78 q^{59} - 34 q^{61} + 20 q^{65} + 162 q^{67} + 252 q^{71} - 12 q^{77} + 158 q^{83} + 108 q^{85} + 4 q^{91} - 4 q^{97} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{3}^{\mathrm{new}}(576, [\chi])\) into newform subspaces

Label Char Prim Dim $A$ Field CM Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
576.3.m.a 576.m 16.f $6$ $15.695$ 6.0.399424.1 None \(0\) \(0\) \(2\) \(4\) $\mathrm{SU}(2)[C_{4}]$ \(q+(1-\beta _{1}+\beta _{2}+\beta _{4})q^{5}+(-\beta _{2}-\beta _{3}+\cdots)q^{7}+\cdots\)
576.3.m.b 576.m 16.f $16$ $15.695$ \(\mathbb{Q}[x]/(x^{16} - \cdots)\) None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{4}]$ \(q+\beta _{3}q^{5}-\beta _{8}q^{7}+(\beta _{4}+\beta _{14})q^{11}+\cdots\)
576.3.m.c 576.m 16.f $16$ $15.695$ \(\mathbb{Q}[x]/(x^{16} - \cdots)\) None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{4}]$ \(q-\beta _{11}q^{5}-\beta _{3}q^{7}+(2+2\beta _{2}-\beta _{5}+\cdots)q^{11}+\cdots\)

Decomposition of \(S_{3}^{\mathrm{old}}(576, [\chi])\) into lower level spaces

\( S_{3}^{\mathrm{old}}(576, [\chi]) \cong \) \(S_{3}^{\mathrm{new}}(16, [\chi])\)\(^{\oplus 9}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(32, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(48, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(64, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(96, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(144, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(192, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(288, [\chi])\)\(^{\oplus 2}\)