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Properties

Label 1045.2.bd
Level $1045$
Weight $2$
Character orbit 1045.bd
Rep. character $\chi_{1045}(12,\cdot)$
Character field $\Q(\zeta_{12})$
Dimension $400$
Sturm bound $240$

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Defining parameters

Level: \( N \) \(=\) \( 1045 = 5 \cdot 11 \cdot 19 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1045.bd (of order \(12\) and degree \(4\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 95 \)
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 496 400 96
Cusp forms 464 400 64
Eisenstein series 32 0 32

Trace form

\( 400 q + 8 q^{6} + O(q^{10}) \) \( 400 q + 8 q^{6} + 36 q^{15} + 176 q^{16} - 12 q^{17} - 48 q^{21} + 8 q^{23} - 12 q^{28} + 72 q^{32} - 60 q^{35} - 168 q^{36} - 68 q^{38} + 72 q^{40} - 88 q^{45} - 64 q^{47} - 84 q^{48} - 76 q^{57} + 96 q^{58} - 144 q^{60} - 80 q^{61} - 80 q^{63} + 96 q^{68} - 348 q^{72} + 64 q^{73} + 56 q^{76} - 120 q^{78} - 12 q^{80} + 216 q^{81} - 80 q^{82} - 8 q^{83} - 168 q^{86} + 208 q^{87} - 60 q^{90} + 4 q^{92} + 48 q^{93} - 8 q^{95} + 32 q^{96} + 36 q^{97} + 144 q^{98} + O(q^{100}) \)

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

\( S_{2}^{\mathrm{old}}(1045, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(95, [\chi])\)\(^{\oplus 2}\)