Properties

Label 930.2.r
Level $930$
Weight $2$
Character orbit 930.r
Rep. character $\chi_{930}(119,\cdot)$
Character field $\Q(\zeta_{6})$
Dimension $128$
Newform subspaces $2$
Sturm bound $384$
Trace bound $2$

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Defining parameters

Level: \( N \) \(=\) \( 930 = 2 \cdot 3 \cdot 5 \cdot 31 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 930.r (of order \(6\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 465 \)
Character field: \(\Q(\zeta_{6})\)
Newform subspaces: \( 2 \)
Sturm bound: \(384\)
Trace bound: \(2\)

Dimensions

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

Total New Old
Modular forms 400 128 272
Cusp forms 368 128 240
Eisenstein series 32 0 32

Trace form

\( 128q + 128q^{4} - 8q^{9} + O(q^{10}) \) \( 128q + 128q^{4} - 8q^{9} + 4q^{10} + 128q^{16} + 8q^{19} + 4q^{25} + 36q^{31} + 12q^{34} - 8q^{36} - 16q^{39} + 4q^{40} + 14q^{45} + 60q^{49} - 16q^{51} + 128q^{64} - 16q^{66} - 20q^{69} + 32q^{70} - 48q^{75} + 8q^{76} - 60q^{79} - 24q^{81} + 4q^{90} - 8q^{94} - 204q^{99} + O(q^{100}) \)

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.r.a \(64\) \(7.426\) None \(-64\) \(0\) \(-2\) \(0\)
930.2.r.b \(64\) \(7.426\) None \(64\) \(0\) \(2\) \(0\)

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

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