↑

Properties

Label 624.4.cl
Level $624$
Weight $4$
Character orbit 624.cl
Rep. character $\chi_{624}(35,\cdot)$
Character field $\Q(\zeta_{12})$
Dimension $1328$
Sturm bound $448$

Related objects

Downloads

Learn more

Defining parameters

Level: \( N \) \(=\) \( 624 = 2^{4} \cdot 3 \cdot 13 \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 624.cl (of order \(12\) and degree \(4\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 624 \)
Character field: \(\Q(\zeta_{12})\)
Sturm bound: \(448\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{4}(624, [\chi])\).

Total New Old
Modular forms 1360 1360 0
Cusp forms 1328 1328 0
Eisenstein series 32 32 0

Trace form

\( 1328 q - 2 q^{3} - 4 q^{4} + 28 q^{6} - 8 q^{7} + O(q^{10}) \) \( 1328 q - 2 q^{3} - 4 q^{4} + 28 q^{6} - 8 q^{7} - 4 q^{10} + 148 q^{12} - 8 q^{13} - 4 q^{16} + 24 q^{18} - 4 q^{19} + 100 q^{21} - 472 q^{22} - 370 q^{24} + 256 q^{27} + 472 q^{28} + 30 q^{30} - 4 q^{33} - 80 q^{34} - 768 q^{36} - 4 q^{37} + 1192 q^{39} - 1576 q^{40} + 522 q^{42} + 428 q^{43} - 252 q^{45} - 1508 q^{46} + 1240 q^{48} - 30192 q^{49} - 116 q^{51} + 28 q^{52} - 2 q^{54} - 296 q^{55} + 2372 q^{58} - 264 q^{60} - 4 q^{61} + 1064 q^{64} + 4352 q^{66} - 4 q^{67} - 110 q^{69} + 712 q^{70} + 2950 q^{72} - 198 q^{75} - 724 q^{76} - 3852 q^{78} - 4 q^{81} + 6084 q^{82} + 3796 q^{84} + 496 q^{85} - 4 q^{87} - 4096 q^{88} - 15820 q^{90} - 436 q^{91} + 4324 q^{93} + 2304 q^{94} + 584 q^{96} - 8 q^{97} + 13532 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{4}^{\mathrm{new}}(624, [\chi])\) into newform subspaces

The newforms in this space have not yet been added to the LMFDB.