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Properties

Label 1960.2.bp
Level $1960$
Weight $2$
Character orbit 1960.bp
Rep. character $\chi_{1960}(313,\cdot)$
Character field $\Q(\zeta_{12})$
Dimension $240$
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.bp (of order \(12\) and degree \(4\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 35 \)
Character field: \(\Q(\zeta_{12})\)
Sturm bound: \(672\)

Dimensions

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

Total New Old
Modular forms 1472 240 1232
Cusp forms 1216 240 976
Eisenstein series 256 0 256

Trace form

\( 240 q + O(q^{10}) \) \( 240 q - 4 q^{11} - 8 q^{15} - 4 q^{23} + 16 q^{25} + 36 q^{33} - 16 q^{37} + 16 q^{43} - 48 q^{45} - 48 q^{51} + 24 q^{53} + 160 q^{57} + 36 q^{61} - 36 q^{65} + 16 q^{67} + 128 q^{71} + 48 q^{73} + 48 q^{75} + 144 q^{81} + 56 q^{85} + 12 q^{87} + 24 q^{93} - 48 q^{95} + O(q^{100}) \)

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

\( S_{2}^{\mathrm{old}}(1960, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(35, [\chi])\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(70, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(140, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(245, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(280, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(490, [\chi])\)\(^{\oplus 3}\)