Properties

Label 930.4.br
Level $930$
Weight $4$
Character orbit 930.br
Rep. character $\chi_{930}(11,\cdot)$
Character field $\Q(\zeta_{30})$
Dimension $1024$
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.br (of order \(30\) and degree \(8\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 93 \)
Character field: \(\Q(\zeta_{30})\)
Sturm bound: \(768\)

Dimensions

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

Total New Old
Modular forms 4672 1024 3648
Cusp forms 4544 1024 3520
Eisenstein series 128 0 128

Trace form

\( 1024 q + 1024 q^{4} - 56 q^{7} + O(q^{10}) \) \( 1024 q + 1024 q^{4} - 56 q^{7} + 180 q^{13} - 4096 q^{16} - 224 q^{18} + 524 q^{19} + 840 q^{21} + 12800 q^{25} + 120 q^{27} - 2736 q^{28} - 1712 q^{31} - 1072 q^{33} - 504 q^{34} + 972 q^{37} - 608 q^{39} - 1392 q^{42} + 1480 q^{43} - 160 q^{45} + 360 q^{46} + 7608 q^{49} - 704 q^{51} - 720 q^{52} + 360 q^{55} - 7440 q^{57} + 2160 q^{58} - 12192 q^{63} + 16384 q^{64} - 3728 q^{66} + 872 q^{67} - 4924 q^{69} + 896 q^{72} + 6564 q^{73} + 624 q^{76} + 5056 q^{78} - 3316 q^{79} - 4432 q^{81} - 1296 q^{82} - 1760 q^{84} + 5668 q^{87} + 480 q^{90} + 20420 q^{91} + 5880 q^{93} + 7056 q^{94} + 10428 q^{97} + 7296 q^{99} + O(q^{100}) \)

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

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