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Properties

Label 1045.2.p
Level $1045$
Weight $2$
Character orbit 1045.p
Rep. character $\chi_{1045}(791,\cdot)$
Character field $\Q(\zeta_{6})$
Dimension $160$
Sturm bound $240$

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Defining parameters

Level: \( N \) \(=\) \( 1045 = 5 \cdot 11 \cdot 19 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1045.p (of order \(6\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 209 \)
Character field: \(\Q(\zeta_{6})\)
Sturm bound: \(240\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(1045, [\chi])\).

Total New Old
Modular forms 248 160 88
Cusp forms 232 160 72
Eisenstein series 16 0 16

Trace form

\( 160 q + 12 q^{3} - 80 q^{4} + 92 q^{9} + O(q^{10}) \) \( 160 q + 12 q^{3} - 80 q^{4} + 92 q^{9} + 8 q^{11} - 12 q^{14} - 80 q^{16} + 30 q^{22} - 8 q^{23} - 80 q^{25} - 8 q^{26} - 36 q^{34} + 112 q^{36} - 24 q^{38} - 72 q^{42} - 36 q^{44} + 16 q^{47} - 48 q^{48} - 136 q^{49} - 72 q^{53} + 104 q^{58} - 72 q^{59} + 208 q^{64} - 26 q^{66} - 36 q^{67} - 72 q^{70} - 12 q^{71} - 60 q^{77} + 60 q^{78} - 16 q^{80} - 72 q^{81} - 60 q^{82} + 12 q^{86} + 36 q^{89} + 24 q^{91} + 16 q^{92} + 132 q^{97} + 52 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{2}^{\mathrm{new}}(1045, [\chi])\) into newform subspaces

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

Decomposition of \(S_{2}^{\mathrm{old}}(1045, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(1045, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(209, [\chi])\)\(^{\oplus 2}\)