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Properties

Label 1260.2.ea
Level $1260$
Weight $2$
Character orbit 1260.ea
Rep. character $\chi_{1260}(113,\cdot)$
Character field $\Q(\zeta_{12})$
Dimension $144$
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.ea (of order \(12\) and degree \(4\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 45 \)
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 144 1056
Cusp forms 1104 144 960
Eisenstein series 96 0 96

Trace form

\( 144 q + 4 q^{3} + O(q^{10}) \) \( 144 q + 4 q^{3} - 12 q^{11} - 8 q^{15} - 4 q^{21} + 24 q^{23} - 12 q^{25} + 16 q^{27} + 32 q^{33} - 24 q^{37} + 48 q^{41} + 40 q^{45} + 84 q^{47} + 140 q^{51} - 24 q^{55} + 28 q^{57} - 8 q^{63} + 24 q^{65} - 12 q^{67} + 28 q^{75} - 96 q^{81} - 120 q^{83} + 48 q^{85} - 100 q^{87} + 24 q^{91} + 4 q^{93} - 120 q^{95} + 36 q^{97} + O(q^{100}) \)

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

\( S_{2}^{\mathrm{old}}(1260, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(45, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(90, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(180, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(315, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(630, [\chi])\)\(^{\oplus 2}\)