Properties

Label 930.2.bs
Level $930$
Weight $2$
Character orbit 930.bs
Rep. character $\chi_{930}(107,\cdot)$
Character field $\Q(\zeta_{60})$
Dimension $1024$
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.bs (of order \(60\) and degree \(16\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 465 \)
Character field: \(\Q(\zeta_{60})\)
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 3200 1024 2176
Cusp forms 2944 1024 1920
Eisenstein series 256 0 256

Trace form

\( 1024q - 8q^{3} + 24q^{7} + O(q^{10}) \) \( 1024q - 8q^{3} + 24q^{7} + 8q^{10} + 8q^{12} - 8q^{15} + 256q^{16} + 44q^{22} + 16q^{25} - 20q^{27} + 4q^{28} + 48q^{30} - 32q^{31} - 52q^{33} + 112q^{37} + 12q^{42} + 40q^{45} + 24q^{46} - 12q^{48} + 16q^{51} - 20q^{55} - 40q^{57} - 56q^{58} - 12q^{60} + 32q^{61} + 224q^{63} - 32q^{66} + 24q^{67} - 24q^{70} - 88q^{73} + 224q^{75} - 96q^{76} - 32q^{78} + 48q^{81} - 24q^{85} + 20q^{87} - 36q^{88} + 8q^{90} - 80q^{91} - 252q^{93} - 32q^{97} + O(q^{100}) \)

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.bs.a \(1024\) \(7.426\) None \(0\) \(-8\) \(0\) \(24\)

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

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