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Properties

Label 1960.2.ce
Level $1960$
Weight $2$
Character orbit 1960.ce
Rep. character $\chi_{1960}(251,\cdot)$
Character field $\Q(\zeta_{14})$
Dimension $1344$
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.ce (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

\( 1344 q + 224 q^{9} + O(q^{10}) \) \( 1344 q + 224 q^{9} - 70 q^{12} + 64 q^{14} - 8 q^{16} + 20 q^{18} - 24 q^{22} + 84 q^{24} - 224 q^{25} - 82 q^{28} + 40 q^{32} + 28 q^{34} - 40 q^{36} - 64 q^{42} + 64 q^{44} - 20 q^{46} + 16 q^{49} + 80 q^{51} + 106 q^{56} + 32 q^{57} - 28 q^{58} + 70 q^{60} + 48 q^{64} - 42 q^{66} + 8 q^{70} + 44 q^{72} + 28 q^{74} + 124 q^{78} - 184 q^{81} + 70 q^{82} - 122 q^{84} + 128 q^{86} + 62 q^{88} - 272 q^{91} - 122 q^{92} + 294 q^{94} - 364 q^{96} + 34 q^{98} + O(q^{100}) \)

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

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