Properties

Label 930.2.bf
Level $930$
Weight $2$
Character orbit 930.bf
Rep. character $\chi_{930}(377,\cdot)$
Character field $\Q(\zeta_{12})$
Dimension $256$
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.bf (of order \(12\) and degree \(4\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 465 \)
Character field: \(\Q(\zeta_{12})\)
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 800 256 544
Cusp forms 736 256 480
Eisenstein series 64 0 64

Trace form

\( 256q + 8q^{3} - 4q^{7} + O(q^{10}) \) \( 256q + 8q^{3} - 4q^{7} - 8q^{10} - 8q^{12} + 8q^{15} - 256q^{16} - 4q^{22} - 16q^{25} - 40q^{27} - 4q^{28} - 48q^{30} + 32q^{31} - 8q^{33} + 8q^{37} - 12q^{42} - 40q^{45} + 16q^{46} - 8q^{48} - 16q^{51} + 20q^{55} + 40q^{57} + 56q^{58} - 8q^{60} - 32q^{61} + 56q^{63} + 32q^{66} - 24q^{67} + 24q^{70} + 8q^{73} - 4q^{75} + 16q^{76} - 88q^{78} - 48q^{81} + 64q^{85} - 20q^{87} - 4q^{88} - 8q^{90} - 68q^{93} + 152q^{97} + O(q^{100}) \)

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

Label Dim. \(A\) Field CM Traces $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\)
930.2.bf.a \(256\) \(7.426\) None \(0\) \(8\) \(0\) \(-4\)

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

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