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Properties

Label 1960.2.cy
Level $1960$
Weight $2$
Character orbit 1960.cy
Rep. character $\chi_{1960}(221,\cdot)$
Character field $\Q(\zeta_{42})$
Dimension $2688$
Sturm bound $672$

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Defining parameters

Level: \( N \) \(=\) \( 1960 = 2^{3} \cdot 5 \cdot 7^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1960.cy (of order \(42\) and degree \(12\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 392 \)
Character field: \(\Q(\zeta_{42})\)
Sturm bound: \(672\)

Dimensions

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

Total New Old
Modular forms 4080 2688 1392
Cusp forms 3984 2688 1296
Eisenstein series 96 0 96

Trace form

\( 2688 q - 224 q^{9} + O(q^{10}) \) \( 2688 q - 224 q^{9} + 80 q^{12} + 52 q^{14} + 4 q^{16} - 10 q^{18} + 8 q^{20} + 24 q^{22} + 116 q^{24} - 224 q^{25} + 2 q^{26} - 62 q^{28} + 68 q^{34} - 40 q^{36} + 40 q^{38} + 62 q^{42} - 54 q^{44} - 10 q^{46} + 40 q^{47} - 124 q^{48} - 16 q^{49} - 12 q^{52} + 40 q^{54} + 32 q^{55} - 164 q^{56} + 32 q^{57} - 14 q^{58} - 112 q^{60} + 16 q^{62} + 80 q^{63} - 102 q^{66} - 28 q^{68} - 20 q^{70} - 80 q^{71} + 22 q^{72} - 16 q^{73} + 14 q^{74} + 20 q^{76} + 124 q^{78} + 288 q^{81} - 106 q^{82} + 316 q^{84} - 154 q^{86} - 48 q^{87} + 10 q^{88} - 8 q^{89} + 36 q^{90} + 36 q^{92} - 354 q^{94} + 366 q^{96} + 64 q^{97} + 58 q^{98} + O(q^{100}) \)

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

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