Properties

Label 576.3.h
Level $576$
Weight $3$
Character orbit 576.h
Rep. character $\chi_{576}(161,\cdot)$
Character field $\Q$
Dimension $16$
Newform subspaces $2$
Sturm bound $288$
Trace bound $25$

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Defining parameters

Level: \( N \) \(=\) \( 576 = 2^{6} \cdot 3^{2} \)
Weight: \( k \) \(=\) \( 3 \)
Character orbit: \([\chi]\) \(=\) 576.h (of order \(2\) and degree \(1\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 24 \)
Character field: \(\Q\)
Newform subspaces: \( 2 \)
Sturm bound: \(288\)
Trace bound: \(25\)
Distinguishing \(T_p\): \(5\)

Dimensions

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

Total New Old
Modular forms 216 16 200
Cusp forms 168 16 152
Eisenstein series 48 0 48

Trace form

\( 16 q + 80 q^{25} + 176 q^{49} + 320 q^{73} + 256 q^{97}+O(q^{100}) \) Copy content Toggle raw display

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

Label Char Prim Dim $A$ Field CM Minimal twist Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
576.3.h.a 576.h 24.h $8$ $15.695$ \(\Q(\zeta_{24})\) None 576.3.h.a \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+\beta_{2} q^{5}-\beta_1 q^{7}-\beta_{7} q^{11}+3\beta_{3} q^{13}+\cdots\)
576.3.h.b 576.h 24.h $8$ $15.695$ \(\Q(\zeta_{24})\) None 576.3.h.b \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q-\beta_{2} q^{5}+\beta_{4} q^{7}-\beta_{5} q^{11}-\beta_{6} q^{13}+\cdots\)

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

\( S_{3}^{\mathrm{old}}(576, [\chi]) \simeq \) \(S_{3}^{\mathrm{new}}(24, [\chi])\)\(^{\oplus 8}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(72, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(96, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(192, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(288, [\chi])\)\(^{\oplus 2}\)