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Properties

Label 1260.2.en
Level $1260$
Weight $2$
Character orbit 1260.en
Rep. character $\chi_{1260}(157,\cdot)$
Character field $\Q(\zeta_{12})$
Dimension $192$
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.en (of order \(12\) and degree \(4\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 315 \)
Character field: \(\Q(\zeta_{12})\)
Sturm bound: \(576\)

Dimensions

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

Total New Old
Modular forms 1200 192 1008
Cusp forms 1104 192 912
Eisenstein series 96 0 96

Trace form

\( 192 q + O(q^{10}) \) \( 192 q + 8 q^{11} + 6 q^{15} - 18 q^{17} + 12 q^{21} - 16 q^{23} - 36 q^{27} + 30 q^{33} + 12 q^{35} + 12 q^{41} + 18 q^{45} + 20 q^{53} + 4 q^{57} + 36 q^{61} + 36 q^{63} - 8 q^{65} + 16 q^{71} - 16 q^{77} - 8 q^{81} + 84 q^{83} - 6 q^{93} - 32 q^{95} + O(q^{100}) \)

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

\( S_{2}^{\mathrm{old}}(1260, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(315, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(630, [\chi])\)\(^{\oplus 2}\)