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Properties

Label 930.4.r
Level $930$
Weight $4$
Character orbit 930.r
Rep. character $\chi_{930}(119,\cdot)$
Character field $\Q(\zeta_{6})$
Dimension $384$
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.r (of order \(6\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 465 \)
Character field: \(\Q(\zeta_{6})\)
Sturm bound: \(768\)

Dimensions

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

Total New Old
Modular forms 1168 384 784
Cusp forms 1136 384 752
Eisenstein series 32 0 32

Trace form

\( 384 q + 1536 q^{4} - 128 q^{9} + O(q^{10}) \) \( 384 q + 1536 q^{4} - 128 q^{9} + 24 q^{10} + 6144 q^{16} - 144 q^{19} - 168 q^{25} - 492 q^{31} - 216 q^{34} - 512 q^{36} + 608 q^{39} + 96 q^{40} - 1324 q^{45} + 9036 q^{49} + 1124 q^{51} + 5364 q^{55} + 24576 q^{64} + 992 q^{66} + 1012 q^{69} + 96 q^{70} - 4890 q^{75} - 576 q^{76} + 1188 q^{79} + 1848 q^{81} + 2248 q^{90} - 1296 q^{94} + 11748 q^{99} + O(q^{100}) \)

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

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