↑

Properties

Label 1960.2.w
Level $1960$
Weight $2$
Character orbit 1960.w
Rep. character $\chi_{1960}(883,\cdot)$
Character field $\Q(\zeta_{4})$
Dimension $472$
Sturm bound $672$

Related objects

Downloads

Learn more

Defining parameters

Level: \( N \) \(=\) \( 1960 = 2^{3} \cdot 5 \cdot 7^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1960.w (of order \(4\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 40 \)
Character field: \(\Q(i)\)
Sturm bound: \(672\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(1960, [\chi])\).

Total New Old
Modular forms 704 512 192
Cusp forms 640 472 168
Eisenstein series 64 40 24

Trace form

\( 472 q + 2 q^{2} + 4 q^{3} - 16 q^{8} + O(q^{10}) \) \( 472 q + 2 q^{2} + 4 q^{3} - 16 q^{8} - 6 q^{10} + 8 q^{11} + 4 q^{12} + 42 q^{18} + 20 q^{20} + 12 q^{22} + 8 q^{25} + 12 q^{26} - 8 q^{27} - 36 q^{30} + 12 q^{32} + 16 q^{33} - 68 q^{36} + 4 q^{38} + 24 q^{40} + 8 q^{41} + 12 q^{43} + 16 q^{46} + 64 q^{48} - 22 q^{50} + 24 q^{51} - 36 q^{52} - 32 q^{57} - 48 q^{58} + 40 q^{60} + 8 q^{65} - 40 q^{66} + 28 q^{67} + 28 q^{68} - 4 q^{72} + 24 q^{73} - 52 q^{75} + 16 q^{76} + 48 q^{78} + 20 q^{80} - 320 q^{81} + 4 q^{82} - 36 q^{83} - 8 q^{86} + 48 q^{88} - 126 q^{90} + 64 q^{92} + 24 q^{96} - 8 q^{97} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{2}^{\mathrm{new}}(1960, [\chi])\) into newform subspaces

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

Decomposition of \(S_{2}^{\mathrm{old}}(1960, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(1960, [\chi]) \simeq \) \(S_{2}^{\mathrm{new}}(40, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(280, [\chi])\)\(^{\oplus 2}\)