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Properties

Label 1045.4.t
Level $1045$
Weight $4$
Character orbit 1045.t
Rep. character $\chi_{1045}(144,\cdot)$
Character field $\Q(\zeta_{6})$
Dimension $600$
Sturm bound $480$

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Defining parameters

Level: \( N \) \(=\) \( 1045 = 5 \cdot 11 \cdot 19 \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 1045.t (of order \(6\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 95 \)
Character field: \(\Q(\zeta_{6})\)
Sturm bound: \(480\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{4}(1045, [\chi])\).

Total New Old
Modular forms 728 600 128
Cusp forms 712 600 112
Eisenstein series 16 0 16

Trace form

\( 600 q + 1212 q^{4} + 12 q^{6} + 2700 q^{9} + O(q^{10}) \) \( 600 q + 1212 q^{4} + 12 q^{6} + 2700 q^{9} + 6 q^{10} + 356 q^{14} + 4 q^{15} - 4764 q^{16} + 264 q^{19} + 40 q^{20} + 388 q^{24} + 64 q^{25} - 32 q^{29} - 520 q^{30} + 672 q^{31} + 1768 q^{34} + 924 q^{35} - 11232 q^{36} - 64 q^{39} - 48 q^{40} + 512 q^{41} + 2704 q^{45} - 1080 q^{46} - 28248 q^{49} - 1128 q^{50} + 1248 q^{51} - 432 q^{54} + 7488 q^{56} + 3312 q^{59} - 2462 q^{60} + 2688 q^{61} - 43464 q^{64} + 2864 q^{65} - 1472 q^{69} + 4856 q^{70} - 4752 q^{71} + 5860 q^{74} - 8056 q^{75} - 2408 q^{76} + 6360 q^{79} + 1878 q^{80} - 21772 q^{81} - 5976 q^{84} - 576 q^{85} - 3984 q^{86} + 2096 q^{89} - 306 q^{90} - 256 q^{91} - 13256 q^{94} - 5304 q^{95} + 17248 q^{96} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{4}^{\mathrm{new}}(1045, [\chi])\) into newform subspaces

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

Decomposition of \(S_{4}^{\mathrm{old}}(1045, [\chi])\) into lower level spaces

\( S_{4}^{\mathrm{old}}(1045, [\chi]) \cong \) \(S_{4}^{\mathrm{new}}(95, [\chi])\)\(^{\oplus 2}\)