Properties

Label 930.2.bn
Level $930$
Weight $2$
Character orbit 930.bn
Rep. character $\chi_{930}(19,\cdot)$
Character field $\Q(\zeta_{30})$
Dimension $256$
Newform subspaces $2$
Sturm bound $384$
Trace bound $1$

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Defining parameters

Level: \( N \) \(=\) \( 930 = 2 \cdot 3 \cdot 5 \cdot 31 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 930.bn (of order \(30\) and degree \(8\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 155 \)
Character field: \(\Q(\zeta_{30})\)
Newform subspaces: \( 2 \)
Sturm bound: \(384\)
Trace bound: \(1\)
Distinguishing \(T_p\): \(7\)

Dimensions

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

Total New Old
Modular forms 1600 256 1344
Cusp forms 1472 256 1216
Eisenstein series 128 0 128

Trace form

\( 256q + 64q^{4} - 16q^{6} - 32q^{9} + O(q^{10}) \) \( 256q + 64q^{4} - 16q^{6} - 32q^{9} - 4q^{10} + 8q^{15} - 64q^{16} - 8q^{19} + 56q^{21} - 4q^{24} + 24q^{25} + 16q^{29} - 8q^{30} - 4q^{31} + 20q^{34} - 40q^{35} - 128q^{36} + 32q^{39} - 6q^{40} + 24q^{41} - 4q^{46} - 40q^{49} + 40q^{50} + 8q^{54} - 96q^{55} + 88q^{59} - 8q^{60} + 176q^{61} + 64q^{64} - 152q^{65} + 12q^{66} + 16q^{70} + 256q^{71} - 24q^{75} + 48q^{76} - 24q^{79} + 32q^{81} - 16q^{84} + 92q^{85} - 136q^{86} + 88q^{89} + 4q^{90} - 48q^{91} + 24q^{94} + 52q^{95} + 4q^{96} + O(q^{100}) \)

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.bn.a \(112\) \(7.426\) None \(0\) \(0\) \(-2\) \(0\)
930.2.bn.b \(144\) \(7.426\) None \(0\) \(0\) \(2\) \(0\)

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

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