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Properties

Label 576.4.k
Level $576$
Weight $4$
Character orbit 576.k
Rep. character $\chi_{576}(145,\cdot)$
Character field $\Q(\zeta_{4})$
Dimension $58$
Newform subspaces $3$
Sturm bound $384$
Trace bound $11$

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Defining parameters

Level: \( N \) \(=\) \( 576 = 2^{6} \cdot 3^{2} \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 576.k (of order \(4\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 16 \)
Character field: \(\Q(i)\)
Newform subspaces: \( 3 \)
Sturm bound: \(384\)
Trace bound: \(11\)
Distinguishing \(T_p\): \(5\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{4}(576, [\chi])\).

Total New Old
Modular forms 608 62 546
Cusp forms 544 58 486
Eisenstein series 64 4 60

Trace form

\( 58 q + 2 q^{5} + O(q^{10}) \) \( 58 q + 2 q^{5} - 22 q^{11} - 2 q^{13} + 4 q^{17} - 22 q^{19} - 198 q^{29} - 368 q^{31} + 20 q^{35} - 10 q^{37} - 26 q^{43} - 944 q^{47} - 2258 q^{49} - 374 q^{53} + 330 q^{59} - 914 q^{61} - 484 q^{65} - 1126 q^{67} - 1636 q^{77} - 1248 q^{79} + 118 q^{83} - 492 q^{85} + 268 q^{91} - 828 q^{95} - 4 q^{97} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{4}^{\mathrm{new}}(576, [\chi])\) into newform subspaces

Label Char Prim Dim $A$ Field CM Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
576.4.k.a 576.k 16.e $10$ $33.985$ \(\mathbb{Q}[x]/(x^{10} - \cdots)\) None \(0\) \(0\) \(2\) \(0\) $\mathrm{SU}(2)[C_{4}]$ \(q-\beta _{3}q^{5}+(3\beta _{1}-\beta _{4})q^{7}+(1-\beta _{1}+\beta _{2}+\cdots)q^{11}+\cdots\)
576.4.k.b 576.k 16.e $24$ $33.985$ None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{4}]$
576.4.k.c 576.k 16.e $24$ $33.985$ None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{4}]$

Decomposition of \(S_{4}^{\mathrm{old}}(576, [\chi])\) into lower level spaces

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