Properties

Label 864.3.g
Level $864$
Weight $3$
Character orbit 864.g
Rep. character $\chi_{864}(703,\cdot)$
Character field $\Q$
Dimension $32$
Newform subspaces $4$
Sturm bound $432$
Trace bound $13$

Related objects

Downloads

Learn more

Defining parameters

Level: \( N \) \(=\) \( 864 = 2^{5} \cdot 3^{3} \)
Weight: \( k \) \(=\) \( 3 \)
Character orbit: \([\chi]\) \(=\) 864.g (of order \(2\) and degree \(1\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 4 \)
Character field: \(\Q\)
Newform subspaces: \( 4 \)
Sturm bound: \(432\)
Trace bound: \(13\)
Distinguishing \(T_p\): \(5\)

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

\( 32 q + O(q^{10}) \) \( 32 q - 16 q^{13} + 144 q^{25} - 144 q^{37} - 288 q^{49} - 208 q^{61} + 192 q^{73} + 480 q^{85} - 64 q^{97} + O(q^{100}) \)

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.g.a 864.g 4.b $8$ $23.542$ 8.0.22581504.2 None \(0\) \(0\) \(-8\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+(-1+\beta _{2})q^{5}+\beta _{7}q^{7}+(\beta _{3}+\beta _{6}+\cdots)q^{11}+\cdots\)
864.3.g.b 864.g 4.b $8$ $23.542$ 8.0.56070144.2 None \(0\) \(0\) \(-8\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+(-1-\beta _{3})q^{5}+(-\beta _{2}-\beta _{6})q^{7}+(-\beta _{2}+\cdots)q^{11}+\cdots\)
864.3.g.c 864.g 4.b $8$ $23.542$ 8.0.22581504.2 None \(0\) \(0\) \(8\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+(1-\beta _{2})q^{5}-\beta _{6}q^{7}+(-\beta _{4}-\beta _{5}+\cdots)q^{11}+\cdots\)
864.3.g.d 864.g 4.b $8$ $23.542$ 8.0.56070144.2 None \(0\) \(0\) \(8\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+(1+\beta _{3})q^{5}+(\beta _{2}+\beta _{6})q^{7}+(-\beta _{2}+\cdots)q^{11}+\cdots\)

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

\( S_{3}^{\mathrm{old}}(864, [\chi]) \cong \) \(S_{3}^{\mathrm{new}}(12, [\chi])\)\(^{\oplus 12}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(16, [\chi])\)\(^{\oplus 8}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(32, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(36, [\chi])\)\(^{\oplus 8}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(48, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(96, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(108, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(144, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(288, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(432, [\chi])\)\(^{\oplus 2}\)