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Properties

Label 930.4.bn
Level $930$
Weight $4$
Character orbit 930.bn
Rep. character $\chi_{930}(19,\cdot)$
Character field $\Q(\zeta_{30})$
Dimension $768$
Sturm bound $768$

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Defining parameters

Level: \( N \) \(=\) \( 930 = 2 \cdot 3 \cdot 5 \cdot 31 \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 930.bn (of order \(30\) and degree \(8\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 155 \)
Character field: \(\Q(\zeta_{30})\)
Sturm bound: \(768\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{4}(930, [\chi])\).

Total New Old
Modular forms 4672 768 3904
Cusp forms 4544 768 3776
Eisenstein series 128 0 128

Trace form

\( 768 q + 768 q^{4} + 96 q^{6} - 864 q^{9} + O(q^{10}) \) \( 768 q + 768 q^{4} + 96 q^{6} - 864 q^{9} - 24 q^{10} + 168 q^{15} - 3072 q^{16} + 144 q^{19} - 744 q^{21} + 96 q^{24} - 376 q^{25} - 1216 q^{29} - 48 q^{30} + 92 q^{31} - 104 q^{34} - 128 q^{35} - 13824 q^{36} + 2064 q^{39} - 144 q^{40} + 768 q^{41} + 2552 q^{46} - 4824 q^{49} - 1744 q^{50} - 432 q^{54} + 1128 q^{55} + 3440 q^{59} - 672 q^{60} - 13440 q^{61} + 12288 q^{64} + 5516 q^{65} + 936 q^{66} - 5184 q^{70} + 5936 q^{71} + 1584 q^{75} - 3456 q^{76} + 8 q^{79} + 7776 q^{81} + 1056 q^{84} + 1620 q^{85} - 2672 q^{86} - 5776 q^{89} + 216 q^{90} - 4720 q^{91} + 368 q^{94} + 2912 q^{95} - 384 q^{96} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{4}^{\mathrm{new}}(930, [\chi])\) into newform subspaces

The newforms in this space have not yet been added to the LMFDB.

Decomposition of \(S_{4}^{\mathrm{old}}(930, [\chi])\) into lower level spaces

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