↑

Properties

Label 1200.4.cf
Level $1200$
Weight $4$
Character orbit 1200.cf
Rep. character $\chi_{1200}(61,\cdot)$
Character field $\Q(\zeta_{20})$
Dimension $2880$
Sturm bound $960$

Related objects

Downloads

Learn more

Defining parameters

Level: \( N \) \(=\) \( 1200 = 2^{4} \cdot 3 \cdot 5^{2} \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 1200.cf (of order \(20\) and degree \(8\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 400 \)
Character field: \(\Q(\zeta_{20})\)
Sturm bound: \(960\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{4}(1200, [\chi])\).

Total New Old
Modular forms 5792 2880 2912
Cusp forms 5728 2880 2848
Eisenstein series 64 0 64

Trace form

\( 2880 q + 252 q^{8} + O(q^{10}) \) \( 2880 q + 252 q^{8} - 12 q^{10} + 48 q^{12} - 432 q^{22} + 40 q^{26} + 408 q^{30} + 1488 q^{31} + 680 q^{32} - 288 q^{34} + 456 q^{35} - 2072 q^{38} + 2356 q^{40} - 1320 q^{42} - 864 q^{43} + 1596 q^{44} + 1056 q^{48} - 141120 q^{49} - 8 q^{50} + 6516 q^{52} - 2016 q^{58} + 1224 q^{60} - 936 q^{62} + 5796 q^{64} + 3904 q^{65} - 5544 q^{67} - 2968 q^{68} - 720 q^{70} + 4312 q^{74} - 1104 q^{75} - 1224 q^{76} + 144 q^{78} - 6320 q^{79} - 712 q^{80} + 58320 q^{81} + 2360 q^{82} - 5360 q^{83} - 2316 q^{88} - 648 q^{90} + 8316 q^{92} - 5476 q^{94} + 7728 q^{95} + 7740 q^{96} - 4288 q^{98} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{4}^{\mathrm{new}}(1200, [\chi])\) into newform subspaces

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

Decomposition of \(S_{4}^{\mathrm{old}}(1200, [\chi])\) into lower level spaces

\( S_{4}^{\mathrm{old}}(1200, [\chi]) \cong \) \(S_{4}^{\mathrm{new}}(400, [\chi])\)\(^{\oplus 2}\)