Properties

Label 930.2.bt
Level $930$
Weight $2$
Character orbit 930.bt
Rep. character $\chi_{930}(13,\cdot)$
Character field $\Q(\zeta_{60})$
Dimension $512$
Newform subspaces $2$
Sturm bound $384$
Trace bound $7$

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Defining parameters

Level: \( N \) \(=\) \( 930 = 2 \cdot 3 \cdot 5 \cdot 31 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 930.bt (of order \(60\) and degree \(16\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 155 \)
Character field: \(\Q(\zeta_{60})\)
Newform subspaces: \( 2 \)
Sturm bound: \(384\)
Trace bound: \(7\)
Distinguishing \(T_p\): \(7\)

Dimensions

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

Total New Old
Modular forms 3200 512 2688
Cusp forms 2944 512 2432
Eisenstein series 256 0 256

Trace form

\( 512q + 24q^{7} + O(q^{10}) \) \( 512q + 24q^{7} + 8q^{10} + 128q^{16} - 32q^{21} + 52q^{22} - 8q^{25} - 4q^{28} - 16q^{31} - 8q^{33} - 48q^{35} + 256q^{36} - 72q^{37} + 32q^{38} + 96q^{41} + 28q^{42} + 96q^{43} - 40q^{46} - 96q^{47} + 96q^{50} - 80q^{53} + 100q^{55} + 24q^{57} - 16q^{62} + 8q^{63} + 96q^{65} + 24q^{66} - 32q^{67} + 88q^{70} - 96q^{71} - 32q^{73} + 96q^{76} - 40q^{77} - 64q^{81} - 16q^{82} + 24q^{83} + 200q^{85} + 48q^{86} + 52q^{87} + 108q^{88} + 80q^{91} + 16q^{93} - 208q^{95} + 16q^{97} + 32q^{98} + O(q^{100}) \)

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.bt.a \(256\) \(7.426\) None \(0\) \(0\) \(0\) \(8\)
930.2.bt.b \(256\) \(7.426\) None \(0\) \(0\) \(0\) \(16\)

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

\( S_{2}^{\mathrm{old}}(930, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(155, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(310, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(465, [\chi])\)\(^{\oplus 2}\)