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Properties

Label 930.2.bk
Level $930$
Weight $2$
Character orbit 930.bk
Rep. character $\chi_{930}(47,\cdot)$
Character field $\Q(\zeta_{20})$
Dimension $512$
Newform subspaces $1$
Sturm bound $384$
Trace bound $0$

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Defining parameters

Level: \( N \) \(=\) \( 930 = 2 \cdot 3 \cdot 5 \cdot 31 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 930.bk (of order \(20\) and degree \(8\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 465 \)
Character field: \(\Q(\zeta_{20})\)
Newform subspaces: \( 1 \)
Sturm bound: \(384\)
Trace bound: \(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(930, [\chi])\).

Total New Old
Modular forms 1600 512 1088
Cusp forms 1472 512 960
Eisenstein series 128 0 128

Trace form

\( 512 q + 8 q^{3} - 12 q^{7} + O(q^{10}) \) \( 512 q + 8 q^{3} - 12 q^{7} - 8 q^{10} - 8 q^{12} + 8 q^{15} + 128 q^{16} + 28 q^{22} + 32 q^{25} + 44 q^{27} + 8 q^{28} + 24 q^{30} + 8 q^{31} + 28 q^{33} + 176 q^{37} + 24 q^{42} - 40 q^{45} - 24 q^{46} + 12 q^{48} - 16 q^{51} - 40 q^{55} + 40 q^{57} + 56 q^{58} + 12 q^{60} - 32 q^{61} - 224 q^{63} + 32 q^{66} + 48 q^{67} + 24 q^{70} + 40 q^{73} - 32 q^{75} + 48 q^{76} - 76 q^{78} - 96 q^{81} + 24 q^{85} - 80 q^{87} - 72 q^{88} + 16 q^{90} + 80 q^{91} - 168 q^{93} - 112 q^{97} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{2}^{\mathrm{new}}(930, [\chi])\) into newform subspaces

Label Char Prim Dim $A$ Field CM Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
930.2.bk.a 930.bk 465.aj $512$ $7.426$ None \(0\) \(8\) \(0\) \(-12\) $\mathrm{SU}(2)[C_{20}]$

Decomposition of \(S_{2}^{\mathrm{old}}(930, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(930, [\chi]) \simeq \) \(S_{2}^{\mathrm{new}}(465, [\chi])\)\(^{\oplus 2}\)