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Properties

Label 1045.4.bh
Level $1045$
Weight $4$
Character orbit 1045.bh
Rep. character $\chi_{1045}(26,\cdot)$
Character field $\Q(\zeta_{15})$
Dimension $1920$
Sturm bound $480$

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Defining parameters

Level: \( N \) \(=\) \( 1045 = 5 \cdot 11 \cdot 19 \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 1045.bh (of order \(15\) and degree \(8\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 209 \)
Character field: \(\Q(\zeta_{15})\)
Sturm bound: \(480\)

Dimensions

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

Total New Old
Modular forms 2912 1920 992
Cusp forms 2848 1920 928
Eisenstein series 64 0 64

Trace form

\( 1920 q - 8 q^{2} - 4 q^{3} + 960 q^{4} + 60 q^{6} + 192 q^{8} + 2220 q^{9} + O(q^{10}) \) \( 1920 q - 8 q^{2} - 4 q^{3} + 960 q^{4} + 60 q^{6} + 192 q^{8} + 2220 q^{9} + 160 q^{10} + 72 q^{11} + 96 q^{12} - 104 q^{13} - 148 q^{14} + 3840 q^{16} + 444 q^{17} - 120 q^{18} + 338 q^{19} - 20 q^{22} + 608 q^{23} + 352 q^{24} + 6000 q^{25} - 144 q^{26} - 2116 q^{27} + 60 q^{29} + 160 q^{30} - 80 q^{31} + 2344 q^{32} + 844 q^{33} + 260 q^{34} - 260 q^{35} + 8188 q^{36} + 672 q^{37} - 750 q^{38} - 360 q^{39} - 480 q^{40} - 526 q^{41} - 2318 q^{42} + 1368 q^{43} + 3584 q^{44} - 2096 q^{46} - 620 q^{47} - 678 q^{48} - 25852 q^{49} + 400 q^{50} + 1058 q^{51} + 486 q^{52} + 1176 q^{53} - 5452 q^{54} + 32 q^{56} - 594 q^{57} + 3952 q^{58} + 1958 q^{59} + 1680 q^{61} + 2100 q^{62} - 1520 q^{63} - 26184 q^{64} - 10000 q^{65} + 236 q^{66} - 1548 q^{67} - 8224 q^{68} + 144 q^{69} - 1620 q^{70} - 500 q^{71} - 488 q^{72} + 2700 q^{73} - 7644 q^{74} - 300 q^{75} + 15024 q^{76} - 7992 q^{77} + 10040 q^{78} + 2520 q^{79} - 3480 q^{80} + 14062 q^{81} + 12084 q^{82} - 9396 q^{83} + 7768 q^{84} - 1376 q^{86} - 5440 q^{87} - 10244 q^{88} + 756 q^{89} - 1960 q^{90} + 4578 q^{91} + 3496 q^{92} + 2160 q^{93} - 13584 q^{94} - 4248 q^{96} - 2490 q^{97} + 8524 q^{98} - 7218 q^{99} + O(q^{100}) \)

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

\( S_{4}^{\mathrm{old}}(1045, [\chi]) \cong \) \(S_{4}^{\mathrm{new}}(209, [\chi])\)\(^{\oplus 2}\)