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Properties

Label 1045.4.i
Level $1045$
Weight $4$
Character orbit 1045.i
Rep. character $\chi_{1045}(771,\cdot)$
Character field $\Q(\zeta_{3})$
Dimension $400$
Sturm bound $480$

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Defining parameters

Level: \( N \) \(=\) \( 1045 = 5 \cdot 11 \cdot 19 \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 1045.i (of order \(3\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 19 \)
Character field: \(\Q(\zeta_{3})\)
Sturm bound: \(480\)

Dimensions

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

Total New Old
Modular forms 728 400 328
Cusp forms 712 400 312
Eisenstein series 16 0 16

Trace form

\( 400 q - 788 q^{4} - 12 q^{6} + 80 q^{7} - 1800 q^{9} + O(q^{10}) \) \( 400 q - 788 q^{4} - 12 q^{6} + 80 q^{7} - 1800 q^{9} - 60 q^{10} - 192 q^{12} + 8 q^{13} - 120 q^{15} - 3236 q^{16} + 64 q^{17} - 816 q^{19} - 264 q^{21} - 88 q^{22} - 160 q^{23} + 360 q^{24} - 5000 q^{25} - 1080 q^{26} - 1112 q^{28} + 160 q^{29} + 96 q^{31} + 140 q^{32} - 264 q^{33} + 1464 q^{34} - 6068 q^{36} + 3520 q^{37} - 1500 q^{38} + 3568 q^{39} - 960 q^{40} - 312 q^{41} - 236 q^{42} - 448 q^{43} - 320 q^{45} - 1880 q^{46} - 772 q^{47} + 1192 q^{48} + 18672 q^{49} - 2328 q^{51} - 736 q^{52} - 392 q^{53} + 1008 q^{54} + 520 q^{56} - 1664 q^{57} - 1384 q^{58} - 616 q^{59} - 1620 q^{60} - 2728 q^{61} + 804 q^{62} - 544 q^{63} + 25168 q^{64} - 1100 q^{66} - 1856 q^{67} + 6184 q^{68} + 3904 q^{69} - 560 q^{70} - 852 q^{71} + 3976 q^{72} - 16 q^{73} + 6352 q^{74} + 5728 q^{76} - 9532 q^{78} + 2752 q^{79} + 880 q^{80} - 18824 q^{81} - 4 q^{82} + 3584 q^{83} - 4328 q^{84} - 240 q^{85} - 776 q^{86} - 4880 q^{87} + 2112 q^{88} - 2508 q^{89} + 180 q^{90} - 1536 q^{91} + 4680 q^{92} - 2472 q^{93} - 6392 q^{94} + 520 q^{95} + 16000 q^{96} + 6340 q^{97} - 16408 q^{98} + O(q^{100}) \)

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

\( S_{4}^{\mathrm{old}}(1045, [\chi]) \cong \) \(S_{4}^{\mathrm{new}}(19, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(209, [\chi])\)\(^{\oplus 2}\)