↑

Properties

Label 930.4.o
Level $930$
Weight $4$
Character orbit 930.o
Rep. character $\chi_{930}(161,\cdot)$
Character field $\Q(\zeta_{6})$
Dimension $256$
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.o (of order \(6\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 93 \)
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 256 912
Cusp forms 1136 256 880
Eisenstein series 32 0 32

Trace form

\( 256 q - 1024 q^{4} + 56 q^{7} + O(q^{10}) \) \( 256 q - 1024 q^{4} + 56 q^{7} - 180 q^{13} + 4096 q^{16} + 224 q^{18} - 524 q^{19} - 840 q^{21} + 3200 q^{25} - 224 q^{28} - 688 q^{31} + 112 q^{33} - 216 q^{34} - 972 q^{37} + 608 q^{39} + 1392 q^{42} + 60 q^{43} + 160 q^{45} - 7608 q^{49} - 3296 q^{51} + 720 q^{52} + 540 q^{55} + 60 q^{57} + 2752 q^{63} - 16384 q^{64} - 1472 q^{66} - 872 q^{67} + 1724 q^{69} - 896 q^{72} - 2724 q^{73} + 2096 q^{76} + 864 q^{78} + 1956 q^{79} - 3768 q^{81} - 144 q^{82} + 3360 q^{84} + 332 q^{87} - 80 q^{90} + 920 q^{93} + 144 q^{94} + 15032 q^{97} + 7704 q^{99} + O(q^{100}) \)

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

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