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Properties

Label 576.5.m
Level $576$
Weight $5$
Character orbit 576.m
Rep. character $\chi_{576}(271,\cdot)$
Character field $\Q(\zeta_{4})$
Dimension $78$
Newform subspaces $3$
Sturm bound $480$
Trace bound $11$

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Defining parameters

Level: \( N \) \(=\) \( 576 = 2^{6} \cdot 3^{2} \)
Weight: \( k \) \(=\) \( 5 \)
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: \(480\)
Trace bound: \(11\)
Distinguishing \(T_p\): \(5\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{5}(576, [\chi])\).

Total New Old
Modular forms 800 82 718
Cusp forms 736 78 658
Eisenstein series 64 4 60

Trace form

\( 78 q + 2 q^{5} + 4 q^{7} + O(q^{10}) \) \( 78 q + 2 q^{5} + 4 q^{7} - 98 q^{11} - 2 q^{13} + 4 q^{17} - 702 q^{19} - 1156 q^{23} + 866 q^{29} - 3844 q^{35} - 1826 q^{37} + 7266 q^{43} + 22634 q^{49} - 478 q^{53} - 11772 q^{55} + 10270 q^{59} + 3774 q^{61} - 2012 q^{65} - 446 q^{67} - 19972 q^{71} + 100 q^{77} + 6718 q^{83} - 12452 q^{85} - 3836 q^{91} - 4 q^{97} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{5}^{\mathrm{new}}(576, [\chi])\) into newform subspaces

Label Char Prim Dim $A$ Field CM Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
576.5.m.a 576.m 16.f $14$ $59.541$ \(\mathbb{Q}[x]/(x^{14} - \cdots)\) None \(0\) \(0\) \(2\) \(4\) $\mathrm{SU}(2)[C_{4}]$ \(q-\beta _{3}q^{5}+\beta _{9}q^{7}+(7-7\beta _{1}+\beta _{7}+\beta _{8}+\cdots)q^{11}+\cdots\)
576.5.m.b 576.m 16.f $32$ $59.541$ None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{4}]$
576.5.m.c 576.m 16.f $32$ $59.541$ None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{4}]$

Decomposition of \(S_{5}^{\mathrm{old}}(576, [\chi])\) into lower level spaces

\( S_{5}^{\mathrm{old}}(576, [\chi]) \cong \) \(S_{5}^{\mathrm{new}}(16, [\chi])\)\(^{\oplus 9}\)\(\oplus\)\(S_{5}^{\mathrm{new}}(32, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{5}^{\mathrm{new}}(48, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{5}^{\mathrm{new}}(64, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{5}^{\mathrm{new}}(96, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{5}^{\mathrm{new}}(144, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{5}^{\mathrm{new}}(192, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{5}^{\mathrm{new}}(288, [\chi])\)\(^{\oplus 2}\)