Properties

Label 930.2.be
Level $930$
Weight $2$
Character orbit 930.be
Rep. character $\chi_{930}(37,\cdot)$
Character field $\Q(\zeta_{12})$
Dimension $128$
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.be (of order \(12\) and degree \(4\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 155 \)
Character field: \(\Q(\zeta_{12})\)
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 800 128 672
Cusp forms 736 128 608
Eisenstein series 64 0 64

Trace form

\( 128q - 4q^{7} + O(q^{10}) \) \( 128q - 4q^{7} - 8q^{10} - 128q^{16} - 48q^{21} - 12q^{22} + 8q^{25} + 4q^{28} + 16q^{31} + 8q^{33} + 48q^{35} + 64q^{36} + 72q^{37} - 32q^{38} - 16q^{41} + 12q^{42} - 96q^{43} + 16q^{47} - 16q^{50} + 60q^{55} - 24q^{57} + 16q^{62} - 8q^{63} + 144q^{65} + 16q^{66} + 32q^{67} - 88q^{70} + 16q^{71} - 48q^{73} - 16q^{76} + 64q^{81} + 16q^{82} - 24q^{83} - 48q^{86} - 52q^{87} + 12q^{88} + 24q^{93} + 128q^{95} - 136q^{97} - 32q^{98} + O(q^{100}) \)

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.be.a \(64\) \(7.426\) None \(0\) \(0\) \(0\) \(-8\)
930.2.be.b \(64\) \(7.426\) None \(0\) \(0\) \(0\) \(4\)

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

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