Properties

Label 1960.2.s
Level $1960$
Weight $2$
Character orbit 1960.s
Rep. character $\chi_{1960}(293,\cdot)$
Character field $\Q(\zeta_{4})$
Dimension $464$
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.s (of order \(4\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 280 \)
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 704 496 208
Cusp forms 640 464 176
Eisenstein series 64 32 32

Trace form

\( 464q + 4q^{2} + 4q^{8} + O(q^{10}) \) \( 464q + 4q^{2} + 4q^{8} - 16q^{15} + 24q^{16} + 32q^{18} - 16q^{22} + 8q^{23} + 8q^{25} + 64q^{30} + 44q^{32} - 48q^{36} - 40q^{46} + 68q^{50} - 40q^{57} + 92q^{58} - 12q^{60} + 8q^{65} + 32q^{71} - 24q^{72} + 72q^{78} - 288q^{81} + 48q^{86} - 24q^{88} + 12q^{92} + 40q^{95} + O(q^{100}) \)

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

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