↑

Properties

Label 1200.2.s
Level $1200$
Weight $2$
Character orbit 1200.s
Rep. character $\chi_{1200}(301,\cdot)$
Character field $\Q(\zeta_{4})$
Dimension $152$
Sturm bound $480$

Related objects

Downloads

Learn more

Defining parameters

Level: \( N \) \(=\) \( 1200 = 2^{4} \cdot 3 \cdot 5^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1200.s (of order \(4\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 16 \)
Character field: \(\Q(i)\)
Sturm bound: \(480\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(1200, [\chi])\).

Total New Old
Modular forms 504 152 352
Cusp forms 456 152 304
Eisenstein series 48 0 48

Trace form

\( 152 q - 4 q^{4} + 12 q^{8} + O(q^{10}) \) \( 152 q - 4 q^{4} + 12 q^{8} - 8 q^{11} - 8 q^{12} - 20 q^{14} + 8 q^{16} + 4 q^{18} + 8 q^{19} - 16 q^{22} - 4 q^{24} - 20 q^{26} + 8 q^{28} - 16 q^{29} - 24 q^{31} + 40 q^{32} + 40 q^{34} + 4 q^{36} - 16 q^{37} + 48 q^{38} + 20 q^{42} + 24 q^{43} + 48 q^{44} + 16 q^{48} - 152 q^{49} - 8 q^{51} + 72 q^{52} + 16 q^{53} - 4 q^{54} + 24 q^{56} - 48 q^{58} - 32 q^{59} - 16 q^{61} + 60 q^{62} + 8 q^{63} - 88 q^{64} - 24 q^{66} + 32 q^{67} - 24 q^{68} - 16 q^{69} - 4 q^{72} - 12 q^{74} - 40 q^{76} + 16 q^{77} + 36 q^{78} + 24 q^{79} - 152 q^{81} - 80 q^{82} + 40 q^{83} - 24 q^{84} - 48 q^{86} - 40 q^{88} + 56 q^{91} - 88 q^{92} + 48 q^{94} - 40 q^{96} + 24 q^{98} - 8 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{2}^{\mathrm{new}}(1200, [\chi])\) into newform subspaces

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

Decomposition of \(S_{2}^{\mathrm{old}}(1200, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(1200, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(16, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(48, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(80, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(240, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(400, [\chi])\)\(^{\oplus 2}\)