Properties

Label 656.2.bs
Level $656$
Weight $2$
Character orbit 656.bs
Rep. character $\chi_{656}(33,\cdot)$
Character field $\Q(\zeta_{20})$
Dimension $160$
Newform subspaces $6$
Sturm bound $168$
Trace bound $3$

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Defining parameters

Level: \( N \) \(=\) \( 656 = 2^{4} \cdot 41 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 656.bs (of order \(20\) and degree \(8\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 41 \)
Character field: \(\Q(\zeta_{20})\)
Newform subspaces: \( 6 \)
Sturm bound: \(168\)
Trace bound: \(3\)
Distinguishing \(T_p\): \(3\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(656, [\chi])\).

Total New Old
Modular forms 720 176 544
Cusp forms 624 160 464
Eisenstein series 96 16 80

Trace form

\( 160 q + 8 q^{3} - 10 q^{5} + 8 q^{7} + O(q^{10}) \) \( 160 q + 8 q^{3} - 10 q^{5} + 8 q^{7} + 8 q^{11} - 6 q^{13} + 14 q^{15} - 10 q^{17} + 8 q^{19} - 10 q^{21} - 6 q^{23} + 22 q^{25} - 4 q^{27} - 42 q^{29} - 6 q^{31} - 10 q^{33} + 6 q^{35} - 6 q^{37} + 10 q^{39} + 2 q^{41} + 10 q^{43} + 4 q^{45} + 68 q^{47} - 10 q^{49} - 18 q^{51} - 10 q^{53} + 58 q^{55} - 14 q^{57} - 54 q^{59} - 10 q^{61} - 6 q^{63} + 12 q^{65} + 20 q^{67} + 6 q^{69} + 8 q^{71} + 32 q^{75} - 10 q^{77} - 4 q^{79} - 88 q^{81} + 160 q^{83} - 32 q^{85} + 10 q^{87} - 22 q^{89} - 10 q^{93} + 18 q^{95} + 6 q^{97} - 94 q^{99} + O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(656, [\chi])\) into newform subspaces

Label Char Prim Dim $A$ Field CM Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
656.2.bs.a 656.bs 41.g $8$ $5.238$ \(\Q(\zeta_{20})\) None \(0\) \(-2\) \(0\) \(0\) $\mathrm{SU}(2)[C_{20}]$ \(q+(\zeta_{20}-\zeta_{20}^{3}+\zeta_{20}^{5}-\zeta_{20}^{6}-\zeta_{20}^{7})q^{3}+\cdots\)
656.2.bs.b 656.bs 41.g $16$ $5.238$ \(\mathbb{Q}[x]/(x^{16} - \cdots)\) None \(0\) \(4\) \(0\) \(0\) $\mathrm{SU}(2)[C_{20}]$ \(q+(1-\beta _{4}-\beta _{6}+\beta _{9}-\beta _{12}+\beta _{15})q^{3}+\cdots\)
656.2.bs.c 656.bs 41.g $24$ $5.238$ None \(0\) \(2\) \(0\) \(0\) $\mathrm{SU}(2)[C_{20}]$
656.2.bs.d 656.bs 41.g $24$ $5.238$ None \(0\) \(6\) \(-10\) \(8\) $\mathrm{SU}(2)[C_{20}]$
656.2.bs.e 656.bs 41.g $40$ $5.238$ None \(0\) \(0\) \(0\) \(4\) $\mathrm{SU}(2)[C_{20}]$
656.2.bs.f 656.bs 41.g $48$ $5.238$ None \(0\) \(-2\) \(0\) \(-4\) $\mathrm{SU}(2)[C_{20}]$

Decomposition of \(S_{2}^{\mathrm{old}}(656, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(656, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(328, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(41, [\chi])\)\(^{\oplus 5}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(82, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(164, [\chi])\)\(^{\oplus 3}\)