Properties

Label 930.2.k
Level $930$
Weight $2$
Character orbit 930.k
Rep. character $\chi_{930}(247,\cdot)$
Character field $\Q(\zeta_{4})$
Dimension $64$
Newform subspaces $2$
Sturm bound $384$
Trace bound $15$

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Defining parameters

Level: \( N \) \(=\) \( 930 = 2 \cdot 3 \cdot 5 \cdot 31 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 930.k (of order \(4\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 155 \)
Character field: \(\Q(i)\)
Newform subspaces: \( 2 \)
Sturm bound: \(384\)
Trace bound: \(15\)
Distinguishing \(T_p\): \(13\)

Dimensions

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

Total New Old
Modular forms 400 64 336
Cusp forms 368 64 304
Eisenstein series 32 0 32

Trace form

\( 64q - 8q^{7} + O(q^{10}) \) \( 64q - 8q^{7} + 8q^{10} - 64q^{16} + 16q^{25} + 8q^{28} - 40q^{31} - 8q^{33} - 48q^{35} - 64q^{36} + 32q^{38} - 32q^{41} - 16q^{47} - 32q^{50} + 8q^{62} + 8q^{63} - 16q^{66} + 64q^{67} - 56q^{70} + 32q^{71} - 32q^{76} - 64q^{81} + 32q^{82} + 40q^{87} - 24q^{93} + 64q^{95} - 8q^{97} + 32q^{98} + O(q^{100}) \)

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.k.a \(32\) \(7.426\) None \(0\) \(0\) \(0\) \(-4\)
930.2.k.b \(32\) \(7.426\) None \(0\) \(0\) \(0\) \(-4\)

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

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