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Properties

Label 1045.2.t
Level $1045$
Weight $2$
Character orbit 1045.t
Rep. character $\chi_{1045}(144,\cdot)$
Character field $\Q(\zeta_{6})$
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.t (of order \(6\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 95 \)
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 248 200 48
Cusp forms 232 200 32
Eisenstein series 16 0 16

Trace form

\( 200 q + 96 q^{4} + 4 q^{6} + 100 q^{9} + O(q^{10}) \) \( 200 q + 96 q^{4} + 4 q^{6} + 100 q^{9} - 6 q^{10} - 4 q^{14} - 2 q^{15} - 88 q^{16} - 8 q^{19} + 40 q^{20} + 32 q^{21} + 28 q^{24} - 4 q^{25} + 8 q^{29} - 40 q^{30} - 80 q^{31} - 24 q^{34} - 30 q^{35} - 84 q^{36} - 48 q^{39} + 12 q^{40} - 16 q^{41} + 4 q^{45} - 40 q^{46} - 184 q^{49} + 8 q^{50} - 4 q^{51} - 16 q^{54} - 48 q^{56} - 40 q^{59} + 10 q^{60} - 24 q^{61} - 288 q^{64} + 16 q^{69} - 96 q^{70} + 28 q^{71} + 4 q^{74} + 140 q^{75} + 24 q^{76} - 16 q^{79} + 62 q^{80} + 4 q^{81} + 328 q^{84} - 4 q^{85} + 32 q^{86} - 20 q^{89} + 126 q^{90} - 16 q^{91} + 40 q^{94} - 108 q^{95} - 48 q^{96} + O(q^{100}) \)

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

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