Properties

Label 576.4.d
Level $576$
Weight $4$
Character orbit 576.d
Rep. character $\chi_{576}(289,\cdot)$
Character field $\Q$
Dimension $30$
Newform subspaces $8$
Sturm bound $384$
Trace bound $17$

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Defining parameters

Level: \( N \) \(=\) \( 576 = 2^{6} \cdot 3^{2} \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 576.d (of order \(2\) and degree \(1\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 8 \)
Character field: \(\Q\)
Newform subspaces: \( 8 \)
Sturm bound: \(384\)
Trace bound: \(17\)
Distinguishing \(T_p\): \(5\), \(7\), \(17\)

Dimensions

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

Total New Old
Modular forms 312 30 282
Cusp forms 264 30 234
Eisenstein series 48 0 48

Trace form

\( 30 q + O(q^{10}) \) \( 30 q + 156 q^{17} - 618 q^{25} + 588 q^{41} + 750 q^{49} - 2304 q^{65} + 12 q^{73} + 2412 q^{89} + 3324 q^{97} + O(q^{100}) \)

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

Label Char Prim Dim $A$ Field CM Minimal twist Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
576.4.d.a 576.d 8.b $2$ $33.985$ \(\Q(\sqrt{-1}) \) \(\Q(\sqrt{-2}) \) 64.4.b.a \(0\) \(0\) \(0\) \(0\) $\mathrm{U}(1)[D_{2}]$ \(q+9iq^{11}-90q^{17}-53iq^{19}+5^{3}q^{25}+\cdots\)
576.4.d.b 576.d 8.b $4$ $33.985$ \(\Q(\zeta_{12})\) None 576.4.d.b \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q-2\zeta_{12}^{2}q^{5}+\zeta_{12}q^{7}+6\zeta_{12}^{3}q^{11}+\cdots\)
576.4.d.c 576.d 8.b $4$ $33.985$ \(\Q(\zeta_{12})\) None 192.4.d.c \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q-\zeta_{12}^{2}q^{5}-7\zeta_{12}q^{7}+12\zeta_{12}^{3}q^{11}+\cdots\)
576.4.d.d 576.d 8.b $4$ $33.985$ \(\Q(\zeta_{12})\) \(\Q(\sqrt{-3}) \) 576.4.d.d \(0\) \(0\) \(0\) \(0\) $\mathrm{U}(1)[D_{2}]$ \(q-\zeta_{12}^{2}q^{7}+\zeta_{12}^{3}q^{13}-7\zeta_{12}q^{19}+\cdots\)
576.4.d.e 576.d 8.b $4$ $33.985$ \(\Q(\zeta_{12})\) None 64.4.b.b \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+\zeta_{12}^{2}q^{5}-\zeta_{12}^{3}q^{7}+21\zeta_{12}q^{11}+\cdots\)
576.4.d.f 576.d 8.b $4$ $33.985$ \(\Q(i, \sqrt{11})\) None 192.4.d.b \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q-\beta _{3}q^{5}+\beta _{2}q^{7}+12\beta _{1}q^{11}-4\beta _{3}q^{13}+\cdots\)
576.4.d.g 576.d 8.b $4$ $33.985$ \(\Q(\zeta_{12})\) None 192.4.d.a \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q-3\zeta_{12}^{2}q^{5}+\zeta_{12}q^{7}+2^{4}\zeta_{12}^{2}q^{13}+\cdots\)
576.4.d.h 576.d 8.b $4$ $33.985$ \(\Q(\zeta_{12})\) None 576.4.d.b \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q-2\zeta_{12}^{2}q^{5}+\zeta_{12}q^{7}+6\zeta_{12}^{3}q^{11}+\cdots\)

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

\( S_{4}^{\mathrm{old}}(576, [\chi]) \simeq \) \(S_{4}^{\mathrm{new}}(8, [\chi])\)\(^{\oplus 12}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(16, [\chi])\)\(^{\oplus 9}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(24, [\chi])\)\(^{\oplus 8}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(32, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(48, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(64, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(72, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(96, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(144, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(192, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(288, [\chi])\)\(^{\oplus 2}\)