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Properties

Label 1260.2.bs
Level $1260$
Weight $2$
Character orbit 1260.bs
Rep. character $\chi_{1260}(11,\cdot)$
Character field $\Q(\zeta_{6})$
Dimension $384$
Sturm bound $576$

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Defining parameters

Level: \( N \) \(=\) \( 1260 = 2^{2} \cdot 3^{2} \cdot 5 \cdot 7 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1260.bs (of order \(6\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 252 \)
Character field: \(\Q(\zeta_{6})\)
Sturm bound: \(576\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(1260, [\chi])\).

Total New Old
Modular forms 592 384 208
Cusp forms 560 384 176
Eisenstein series 32 0 32

Trace form

\( 384 q + O(q^{10}) \) \( 384 q + 10 q^{12} + 30 q^{14} + 10 q^{18} - 4 q^{21} + 20 q^{24} + 192 q^{25} + 12 q^{29} - 40 q^{36} + 60 q^{38} + 72 q^{42} - 66 q^{44} - 4 q^{45} + 84 q^{48} - 38 q^{54} + 28 q^{60} - 48 q^{66} - 30 q^{68} - 24 q^{69} - 6 q^{72} - 84 q^{74} + 48 q^{77} - 48 q^{78} + 40 q^{81} + 64 q^{84} - 54 q^{86} + 60 q^{89} + 18 q^{90} - 60 q^{92} - 16 q^{93} - 18 q^{96} - 102 q^{98} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{2}^{\mathrm{new}}(1260, [\chi])\) into newform subspaces

The newforms in this space have not yet been added to the LMFDB.

Decomposition of \(S_{2}^{\mathrm{old}}(1260, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(1260, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(252, [\chi])\)\(^{\oplus 2}\)