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Properties

Label 1260.2.do
Level $1260$
Weight $2$
Character orbit 1260.do
Rep. character $\chi_{1260}(83,\cdot)$
Character field $\Q(\zeta_{12})$
Dimension $1120$
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.do (of order \(12\) and degree \(4\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 1260 \)
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 1184 1184 0
Cusp forms 1120 1120 0
Eisenstein series 64 64 0

Trace form

\( 1120 q - 12 q^{2} + O(q^{10}) \) \( 1120 q - 12 q^{2} - 8 q^{16} - 8 q^{21} + 12 q^{22} - 8 q^{25} + 8 q^{28} - 8 q^{30} + 48 q^{32} - 48 q^{36} - 32 q^{37} + 10 q^{42} - 32 q^{46} - 12 q^{50} + 72 q^{56} + 48 q^{57} + 12 q^{58} - 32 q^{60} + 24 q^{65} - 22 q^{70} - 92 q^{72} - 12 q^{77} - 92 q^{78} + 48 q^{81} - 8 q^{85} - 240 q^{86} - 36 q^{88} - 12 q^{92} + 8 q^{93} + O(q^{100}) \)

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.