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Properties

Label 930.4.h
Level $930$
Weight $4$
Character orbit 930.h
Rep. character $\chi_{930}(371,\cdot)$
Character field $\Q$
Dimension $128$
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.h (of order \(2\) and degree \(1\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 93 \)
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 584 128 456
Cusp forms 568 128 440
Eisenstein series 16 0 16

Trace form

\( 128 q - 512 q^{4} + 40 q^{7} + O(q^{10}) \) \( 128 q - 512 q^{4} + 40 q^{7} + 2048 q^{16} - 224 q^{18} + 632 q^{19} - 3200 q^{25} - 160 q^{28} - 128 q^{31} - 112 q^{33} + 304 q^{39} - 160 q^{45} + 3960 q^{49} + 3296 q^{51} + 2048 q^{63} - 8192 q^{64} + 3872 q^{66} - 1816 q^{67} - 344 q^{69} + 896 q^{72} - 2528 q^{76} - 3120 q^{78} + 2976 q^{81} - 288 q^{82} + 40 q^{87} - 160 q^{90} - 2312 q^{93} + 2016 q^{94} - 9488 q^{97} + O(q^{100}) \)

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

\( S_{4}^{\mathrm{old}}(930, [\chi]) \cong \) \(S_{4}^{\mathrm{new}}(93, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(186, [\chi])\)\(^{\oplus 2}\)