Properties

Label 864.3.e
Level $864$
Weight $3$
Character orbit 864.e
Rep. character $\chi_{864}(161,\cdot)$
Character field $\Q$
Dimension $32$
Newform subspaces $6$
Sturm bound $432$
Trace bound $13$

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Defining parameters

Level: \( N \) \(=\) \( 864 = 2^{5} \cdot 3^{3} \)
Weight: \( k \) \(=\) \( 3 \)
Character orbit: \([\chi]\) \(=\) 864.e (of order \(2\) and degree \(1\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 3 \)
Character field: \(\Q\)
Newform subspaces: \( 6 \)
Sturm bound: \(432\)
Trace bound: \(13\)
Distinguishing \(T_p\): \(5\), \(7\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{3}(864, [\chi])\).

Total New Old
Modular forms 312 32 280
Cusp forms 264 32 232
Eisenstein series 48 0 48

Trace form

\( 32 q + O(q^{10}) \) \( 32 q + 16 q^{13} - 176 q^{25} - 16 q^{37} + 320 q^{49} - 208 q^{61} - 192 q^{73} + 416 q^{85} + 160 q^{97} + O(q^{100}) \)

Decomposition of \(S_{3}^{\mathrm{new}}(864, [\chi])\) into newform subspaces

Label Char Prim Dim $A$ Field CM Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
864.3.e.a 864.e 3.b $4$ $23.542$ \(\Q(\sqrt{-2}, \sqrt{-5})\) None \(0\) \(0\) \(0\) \(-12\) $\mathrm{SU}(2)[C_{2}]$ \(q-\beta _{3}q^{5}+(-3+\beta _{1})q^{7}+(-\beta _{2}-3\beta _{3})q^{11}+\cdots\)
864.3.e.b 864.e 3.b $4$ $23.542$ \(\Q(\zeta_{8})\) None \(0\) \(0\) \(0\) \(-12\) $\mathrm{SU}(2)[C_{2}]$ \(q+(\zeta_{8}+\zeta_{8}^{2})q^{5}+(-3-\zeta_{8}^{3})q^{7}+(-\zeta_{8}+\cdots)q^{11}+\cdots\)
864.3.e.c 864.e 3.b $4$ $23.542$ \(\Q(\sqrt{-2}, \sqrt{-5})\) None \(0\) \(0\) \(0\) \(12\) $\mathrm{SU}(2)[C_{2}]$ \(q+\beta _{3}q^{5}+(3+\beta _{1})q^{7}+(\beta _{2}-3\beta _{3})q^{11}+\cdots\)
864.3.e.d 864.e 3.b $4$ $23.542$ \(\Q(\zeta_{8})\) None \(0\) \(0\) \(0\) \(12\) $\mathrm{SU}(2)[C_{2}]$ \(q+(\zeta_{8}+\zeta_{8}^{2})q^{5}+(3+\zeta_{8}^{3})q^{7}+(\zeta_{8}+\cdots)q^{11}+\cdots\)
864.3.e.e 864.e 3.b $8$ $23.542$ 8.0.2441150464.4 None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q-\beta _{6}q^{5}+\beta _{4}q^{7}+(\beta _{1}+\beta _{2})q^{11}+(-2+\cdots)q^{13}+\cdots\)
864.3.e.f 864.e 3.b $8$ $23.542$ \(\Q(\zeta_{24})\) None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+\zeta_{24}^{2}q^{5}-\zeta_{24}^{4}q^{7}-\zeta_{24}^{6}q^{11}+\cdots\)

Decomposition of \(S_{3}^{\mathrm{old}}(864, [\chi])\) into lower level spaces

\( S_{3}^{\mathrm{old}}(864, [\chi]) \cong \) \(S_{3}^{\mathrm{new}}(12, [\chi])\)\(^{\oplus 12}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(18, [\chi])\)\(^{\oplus 10}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(24, [\chi])\)\(^{\oplus 9}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(27, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(48, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(54, [\chi])\)\(^{\oplus 5}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(72, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(96, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(108, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(144, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(216, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(288, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(432, [\chi])\)\(^{\oplus 2}\)