↑

Properties

Label 930.4.s
Level $930$
Weight $4$
Character orbit 930.s
Rep. character $\chi_{930}(439,\cdot)$
Character field $\Q(\zeta_{6})$
Dimension $192$
Sturm bound $768$

Related objects

Downloads

Learn more

Defining parameters

Level: \( N \) \(=\) \( 930 = 2 \cdot 3 \cdot 5 \cdot 31 \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 930.s (of order \(6\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 155 \)
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 192 976
Cusp forms 1136 192 944
Eisenstein series 32 0 32

Trace form

\( 192 q - 768 q^{4} + 24 q^{6} + 864 q^{9} + O(q^{10}) \) \( 192 q - 768 q^{4} + 24 q^{6} + 864 q^{9} + 24 q^{10} - 168 q^{15} + 3072 q^{16} - 144 q^{19} + 264 q^{21} - 96 q^{24} + 376 q^{25} - 1024 q^{29} + 48 q^{30} - 92 q^{31} - 616 q^{34} + 128 q^{35} - 3456 q^{36} + 1296 q^{39} - 96 q^{40} - 448 q^{41} - 2192 q^{46} + 4564 q^{49} + 384 q^{50} + 432 q^{54} + 392 q^{55} - 160 q^{59} + 672 q^{60} - 1200 q^{61} - 12288 q^{64} - 3796 q^{65} + 624 q^{66} + 2224 q^{70} + 2624 q^{71} + 1056 q^{75} + 576 q^{76} + 172 q^{79} - 7776 q^{81} - 1056 q^{84} - 1400 q^{85} + 992 q^{86} - 1904 q^{89} - 216 q^{90} - 3440 q^{91} - 368 q^{94} - 3312 q^{95} + 384 q^{96} + O(q^{100}) \)

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

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