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Properties

Label 1045.2.bg
Level $1045$
Weight $2$
Character orbit 1045.bg
Rep. character $\chi_{1045}(87,\cdot)$
Character field $\Q(\zeta_{12})$
Dimension $464$
Sturm bound $240$

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Defining parameters

Level: \( N \) \(=\) \( 1045 = 5 \cdot 11 \cdot 19 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1045.bg (of order \(12\) and degree \(4\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 1045 \)
Character field: \(\Q(\zeta_{12})\)
Sturm bound: \(240\)

Dimensions

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

Total New Old
Modular forms 496 496 0
Cusp forms 464 464 0
Eisenstein series 32 32 0

Trace form

\( 464 q - 4 q^{3} + O(q^{10}) \) \( 464 q - 4 q^{3} - 24 q^{11} - 56 q^{12} - 4 q^{15} + 200 q^{16} + 32 q^{20} + 14 q^{22} - 20 q^{23} + 16 q^{25} - 64 q^{26} - 40 q^{27} - 32 q^{31} - 24 q^{33} + 88 q^{36} + 16 q^{37} + 32 q^{38} + 44 q^{42} + 8 q^{45} + 16 q^{47} + 76 q^{48} - 16 q^{53} - 20 q^{55} - 48 q^{56} - 152 q^{58} - 116 q^{60} - 20 q^{66} - 20 q^{67} - 60 q^{70} - 8 q^{71} - 112 q^{75} + 20 q^{77} + 32 q^{80} + 192 q^{81} + 16 q^{82} - 104 q^{86} + 16 q^{88} - 56 q^{91} + 12 q^{92} - 104 q^{93} + 12 q^{97} + O(q^{100}) \)

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.