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Properties

Label 1045.6.t
Level $1045$
Weight $6$
Character orbit 1045.t
Rep. character $\chi_{1045}(144,\cdot)$
Character field $\Q(\zeta_{6})$
Dimension $1000$
Sturm bound $720$

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Defining parameters

Level: \( N \) \(=\) \( 1045 = 5 \cdot 11 \cdot 19 \)
Weight: \( k \) \(=\) \( 6 \)
Character orbit: \([\chi]\) \(=\) 1045.t (of order \(6\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 95 \)
Character field: \(\Q(\zeta_{6})\)
Sturm bound: \(720\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{6}(1045, [\chi])\).

Total New Old
Modular forms 1208 1000 208
Cusp forms 1192 1000 192
Eisenstein series 16 0 16

Trace form

\( 1000 q + 7980 q^{4} - 180 q^{6} + 40500 q^{9} + O(q^{10}) \) \( 1000 q + 7980 q^{4} - 180 q^{6} + 40500 q^{9} + 534 q^{10} - 5884 q^{14} + 598 q^{15} - 126140 q^{16} - 7240 q^{19} - 3320 q^{20} - 12576 q^{21} - 572 q^{24} - 124 q^{25} - 5672 q^{29} + 49880 q^{30} - 12688 q^{31} - 7736 q^{34} - 30 q^{35} - 641520 q^{36} - 61552 q^{39} - 17088 q^{40} - 10480 q^{41} - 29876 q^{45} + 13000 q^{46} - 2412920 q^{49} - 158952 q^{50} + 2460 q^{51} + 58320 q^{54} - 476928 q^{56} - 200232 q^{59} - 20990 q^{60} - 85320 q^{61} - 3961992 q^{64} - 129760 q^{65} + 303664 q^{69} - 273976 q^{70} + 122124 q^{71} + 70708 q^{74} + 170060 q^{75} - 352520 q^{76} + 127408 q^{79} + 255222 q^{80} - 4071004 q^{81} - 1119768 q^{84} + 140116 q^{85} + 500880 q^{86} - 235276 q^{89} + 582726 q^{90} + 741552 q^{91} + 516216 q^{94} + 274932 q^{95} - 447008 q^{96} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{6}^{\mathrm{new}}(1045, [\chi])\) into newform subspaces

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

Decomposition of \(S_{6}^{\mathrm{old}}(1045, [\chi])\) into lower level spaces

\( S_{6}^{\mathrm{old}}(1045, [\chi]) \cong \) \(S_{6}^{\mathrm{new}}(95, [\chi])\)\(^{\oplus 2}\)