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Properties

Label 930.4.bo
Level $930$
Weight $4$
Character orbit 930.bo
Rep. character $\chi_{930}(179,\cdot)$
Character field $\Q(\zeta_{30})$
Dimension $1536$
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.bo (of order \(30\) and degree \(8\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 465 \)
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 1536 3136
Cusp forms 4544 1536 3008
Eisenstein series 128 0 128

Trace form

\( 1536 q - 1536 q^{4} + 128 q^{9} + O(q^{10}) \) \( 1536 q - 1536 q^{4} + 128 q^{9} - 24 q^{10} + 340 q^{15} - 6144 q^{16} + 144 q^{19} + 168 q^{25} - 228 q^{31} - 504 q^{34} + 512 q^{36} - 608 q^{39} + 144 q^{40} + 1734 q^{45} - 360 q^{46} - 10056 q^{49} + 4756 q^{51} - 5364 q^{55} - 1360 q^{60} - 24576 q^{64} - 992 q^{66} - 1012 q^{69} - 96 q^{70} - 8950 q^{75} + 3456 q^{76} - 6048 q^{79} - 1848 q^{81} + 6300 q^{85} + 6772 q^{90} - 7920 q^{91} + 1296 q^{94} - 11748 q^{99} + O(q^{100}) \)

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

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