Properties

Label 930.4.i
Level $930$
Weight $4$
Character orbit 930.i
Rep. character $\chi_{930}(211,\cdot)$
Character field $\Q(\zeta_{3})$
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.i (of order \(3\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 31 \)
Character field: \(\Q(\zeta_{3})\)
Sturm bound: \(768\)

Dimensions

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

Total New Old
Modular forms 1168 128 1040
Cusp forms 1136 128 1008
Eisenstein series 32 0 32

Trace form

\( 128 q + 12 q^{3} + 512 q^{4} - 8 q^{7} - 576 q^{9} + O(q^{10}) \) \( 128 q + 12 q^{3} + 512 q^{4} - 8 q^{7} - 576 q^{9} - 80 q^{11} + 48 q^{12} + 172 q^{13} - 80 q^{14} + 2048 q^{16} + 80 q^{17} - 44 q^{19} + 24 q^{21} + 288 q^{22} + 224 q^{23} - 1600 q^{25} - 80 q^{26} - 216 q^{27} - 32 q^{28} - 1456 q^{29} - 240 q^{30} - 1144 q^{31} - 768 q^{33} - 72 q^{34} - 320 q^{35} - 2304 q^{36} - 276 q^{37} + 432 q^{38} + 456 q^{39} + 1104 q^{41} + 336 q^{42} + 1548 q^{43} - 320 q^{44} + 16 q^{46} + 2192 q^{47} + 192 q^{48} - 2512 q^{49} + 120 q^{51} + 688 q^{52} + 624 q^{53} + 180 q^{55} - 320 q^{56} + 204 q^{57} - 1248 q^{58} - 24 q^{59} - 1408 q^{61} - 2112 q^{62} + 144 q^{63} + 8192 q^{64} - 144 q^{66} - 3360 q^{67} + 320 q^{68} + 1784 q^{71} - 444 q^{73} + 2160 q^{74} + 300 q^{75} - 176 q^{76} + 7312 q^{77} - 1056 q^{78} + 2276 q^{79} - 5184 q^{81} - 592 q^{82} + 1376 q^{83} + 96 q^{84} - 3600 q^{85} - 2496 q^{86} + 1104 q^{87} + 1152 q^{88} + 928 q^{89} - 7456 q^{91} + 896 q^{92} + 3204 q^{93} + 7152 q^{94} - 4744 q^{97} - 64 q^{98} - 720 q^{99} + O(q^{100}) \)

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

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