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Properties

Label 1045.2.m
Level $1045$
Weight $2$
Character orbit 1045.m
Rep. character $\chi_{1045}(683,\cdot)$
Character field $\Q(\zeta_{4})$
Dimension $200$
Sturm bound $240$

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Defining parameters

Level: \( N \) \(=\) \( 1045 = 5 \cdot 11 \cdot 19 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1045.m (of order \(4\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 95 \)
Character field: \(\Q(i)\)
Sturm bound: \(240\)

Dimensions

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

Total New Old
Modular forms 248 200 48
Cusp forms 232 200 32
Eisenstein series 16 0 16

Trace form

\( 200 q + 16 q^{6} + O(q^{10}) \) \( 200 q + 16 q^{6} - 248 q^{16} - 24 q^{17} + 16 q^{23} - 24 q^{28} + 24 q^{35} + 264 q^{36} + 32 q^{38} - 48 q^{43} + 16 q^{45} - 8 q^{47} + 16 q^{57} + 48 q^{58} + 32 q^{61} - 64 q^{63} - 96 q^{68} - 64 q^{73} + 40 q^{76} - 24 q^{80} - 168 q^{81} - 160 q^{82} + 8 q^{83} - 208 q^{87} + 8 q^{92} + 96 q^{93} + 44 q^{95} - 128 q^{96} + O(q^{100}) \)

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

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