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Properties

Label 930.4.e
Level $930$
Weight $4$
Character orbit 930.e
Rep. character $\chi_{930}(929,\cdot)$
Character field $\Q$
Dimension $192$
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.e (of order \(2\) and degree \(1\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 465 \)
Character field: \(\Q\)
Sturm bound: \(768\)

Dimensions

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

Total New Old
Modular forms 584 192 392
Cusp forms 568 192 376
Eisenstein series 16 0 16

Trace form

\( 192 q + 768 q^{4} + 128 q^{9} + O(q^{10}) \) \( 192 q + 768 q^{4} + 128 q^{9} - 24 q^{10} + 3072 q^{16} - 288 q^{19} - 588 q^{25} + 168 q^{31} + 512 q^{36} + 304 q^{39} - 96 q^{40} - 8 q^{45} - 10152 q^{49} + 2200 q^{51} + 12288 q^{64} - 992 q^{66} - 1768 q^{69} - 96 q^{70} - 1152 q^{76} - 2256 q^{81} + 6056 q^{90} + 1296 q^{94} + O(q^{100}) \)

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

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