Properties

Label 930.4.j
Level $930$
Weight $4$
Character orbit 930.j
Rep. character $\chi_{930}(497,\cdot)$
Character field $\Q(\zeta_{4})$
Dimension $360$
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.j (of order \(4\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 15 \)
Character field: \(\Q(i)\)
Sturm bound: \(768\)

Dimensions

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

Total New Old
Modular forms 1168 360 808
Cusp forms 1136 360 776
Eisenstein series 32 0 32

Trace form

\( 360 q - 16 q^{6} + O(q^{10}) \) \( 360 q - 16 q^{6} + 240 q^{13} + 336 q^{15} - 5760 q^{16} + 32 q^{18} - 928 q^{21} + 528 q^{27} - 1280 q^{33} - 736 q^{36} - 528 q^{37} + 384 q^{40} + 1216 q^{42} + 3936 q^{43} + 896 q^{45} + 2016 q^{46} - 544 q^{51} - 960 q^{52} - 1104 q^{55} - 1616 q^{57} - 2208 q^{58} - 704 q^{60} - 240 q^{61} + 936 q^{63} + 96 q^{66} - 1392 q^{67} + 1728 q^{70} - 128 q^{72} - 1680 q^{73} + 4736 q^{75} + 2848 q^{78} + 4120 q^{81} - 4416 q^{82} + 5040 q^{85} - 7280 q^{87} - 3392 q^{90} - 960 q^{91} + 256 q^{96} + 4416 q^{97} + O(q^{100}) \)

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

\( S_{4}^{\mathrm{old}}(930, [\chi]) \cong \) \(S_{4}^{\mathrm{new}}(15, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(30, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(465, [\chi])\)\(^{\oplus 2}\)