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Properties

Label 930.4.n
Level $930$
Weight $4$
Character orbit 930.n
Rep. character $\chi_{930}(481,\cdot)$
Character field $\Q(\zeta_{5})$
Dimension $256$
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.n (of order \(5\) and degree \(4\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 31 \)
Character field: \(\Q(\zeta_{5})\)
Sturm bound: \(768\)

Dimensions

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

Total New Old
Modular forms 2336 256 2080
Cusp forms 2272 256 2016
Eisenstein series 64 0 64

Trace form

\( 256 q - 12 q^{3} - 256 q^{4} - 56 q^{7} - 576 q^{9} + O(q^{10}) \) \( 256 q - 12 q^{3} - 256 q^{4} - 56 q^{7} - 576 q^{9} - 240 q^{11} - 48 q^{12} - 96 q^{13} - 240 q^{14} - 1024 q^{16} - 152 q^{17} - 152 q^{19} + 252 q^{21} - 48 q^{22} + 928 q^{23} + 6400 q^{25} - 640 q^{26} - 108 q^{27} + 336 q^{28} - 1232 q^{29} - 480 q^{30} - 1040 q^{31} - 576 q^{33} - 216 q^{34} - 240 q^{35} + 9216 q^{36} - 712 q^{37} - 1184 q^{38} - 228 q^{39} + 2512 q^{41} + 336 q^{42} + 956 q^{43} + 640 q^{44} + 856 q^{46} - 352 q^{47} - 192 q^{48} - 480 q^{49} + 960 q^{51} - 384 q^{52} - 808 q^{53} + 540 q^{55} + 640 q^{56} - 2664 q^{57} - 2304 q^{58} - 2192 q^{59} + 4472 q^{61} - 1008 q^{62} - 504 q^{63} - 4096 q^{64} + 1416 q^{66} - 6440 q^{67} - 448 q^{68} + 352 q^{71} + 4736 q^{73} + 2000 q^{74} - 300 q^{75} + 912 q^{76} + 5880 q^{77} + 1584 q^{78} + 3472 q^{79} - 5184 q^{81} + 1904 q^{82} - 3568 q^{83} - 672 q^{84} + 4040 q^{85} + 3632 q^{86} - 2208 q^{87} - 3712 q^{88} - 72 q^{89} - 1436 q^{91} - 448 q^{92} - 492 q^{93} - 7728 q^{94} + 868 q^{97} - 64 q^{98} + 1440 q^{99} + O(q^{100}) \)

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

\( S_{4}^{\mathrm{old}}(930, [\chi]) \cong \) \(S_{4}^{\mathrm{new}}(31, [\chi])\)\(^{\oplus 8}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(62, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(93, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(155, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(186, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(310, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(465, [\chi])\)\(^{\oplus 2}\)