↑

Properties

Label 1960.2.ck
Level $1960$
Weight $2$
Character orbit 1960.ck
Rep. character $\chi_{1960}(141,\cdot)$
Character field $\Q(\zeta_{14})$
Dimension $1344$
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.ck (of order \(14\) and degree \(6\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 392 \)
Character field: \(\Q(\zeta_{14})\)
Sturm bound: \(672\)

Dimensions

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

Total New Old
Modular forms 2040 1344 696
Cusp forms 1992 1344 648
Eisenstein series 48 0 48

Trace form

\( 1344 q + 224 q^{9} + O(q^{10}) \) \( 1344 q + 224 q^{9} - 50 q^{12} - 64 q^{14} + 8 q^{16} - 20 q^{18} - 8 q^{20} - 24 q^{22} - 80 q^{24} + 224 q^{25} + 28 q^{26} + 62 q^{28} + 4 q^{34} + 40 q^{36} + 20 q^{38} + 4 q^{42} - 24 q^{44} - 20 q^{46} - 40 q^{47} + 4 q^{48} + 16 q^{49} - 24 q^{52} - 52 q^{54} + 16 q^{55} + 134 q^{56} - 32 q^{57} - 28 q^{58} + 70 q^{60} - 16 q^{62} + 40 q^{63} + 6 q^{66} + 28 q^{68} + 8 q^{70} + 80 q^{71} + 44 q^{72} - 32 q^{73} + 28 q^{74} + 52 q^{76} - 124 q^{78} - 264 q^{81} - 2 q^{82} + 134 q^{84} - 56 q^{86} + 48 q^{87} + 62 q^{88} - 16 q^{89} - 36 q^{90} - 78 q^{92} + 30 q^{94} + 288 q^{96} + 32 q^{97} - 34 q^{98} + O(q^{100}) \)

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

\( S_{2}^{\mathrm{old}}(1960, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(392, [\chi])\)\(^{\oplus 2}\)