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Properties

Label 1960.2.bg
Level $1960$
Weight $2$
Character orbit 1960.bg
Rep. character $\chi_{1960}(569,\cdot)$
Character field $\Q(\zeta_{6})$
Dimension $120$
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.bg (of order \(6\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 35 \)
Character field: \(\Q(\zeta_{6})\)
Sturm bound: \(672\)

Dimensions

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

Total New Old
Modular forms 736 120 616
Cusp forms 608 120 488
Eisenstein series 128 0 128

Trace form

\( 120 q + 58 q^{9} + O(q^{10}) \) \( 120 q + 58 q^{9} + 2 q^{11} - 20 q^{15} + 10 q^{19} - 2 q^{25} - 12 q^{29} - 4 q^{31} - 40 q^{39} - 24 q^{41} + 8 q^{45} + 12 q^{51} + 12 q^{55} + 48 q^{59} + 18 q^{61} + 18 q^{65} + 60 q^{69} - 32 q^{71} + 14 q^{75} + 48 q^{79} - 108 q^{81} + 116 q^{85} - 30 q^{89} + 42 q^{95} + 68 q^{99} + O(q^{100}) \)

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

\( S_{2}^{\mathrm{old}}(1960, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(35, [\chi])\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(70, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(140, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(245, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(280, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(490, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(980, [\chi])\)\(^{\oplus 2}\)