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Properties

Label 1045.4.cf
Level $1045$
Weight $4$
Character orbit 1045.cf
Rep. character $\chi_{1045}(7,\cdot)$
Character field $\Q(\zeta_{60})$
Dimension $5696$
Sturm bound $480$

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Defining parameters

Level: \( N \) \(=\) \( 1045 = 5 \cdot 11 \cdot 19 \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 1045.cf (of order \(60\) and degree \(16\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 1045 \)
Character field: \(\Q(\zeta_{60})\)
Sturm bound: \(480\)

Dimensions

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

Total New Old
Modular forms 5824 5824 0
Cusp forms 5696 5696 0
Eisenstein series 128 128 0

Trace form

\( 5696 q - 10 q^{2} - 6 q^{3} + 10 q^{5} - 20 q^{6} - 40 q^{8} + O(q^{10}) \) \( 5696 q - 10 q^{2} - 6 q^{3} + 10 q^{5} - 20 q^{6} - 40 q^{8} - 120 q^{11} + 216 q^{12} - 10 q^{13} - 6 q^{15} - 11020 q^{16} - 330 q^{17} - 40 q^{18} - 1792 q^{20} + 92 q^{22} - 128 q^{23} - 446 q^{25} - 2352 q^{26} + 192 q^{27} - 10 q^{28} - 40 q^{30} - 48 q^{31} + 34 q^{33} - 10 q^{35} - 23804 q^{36} - 888 q^{37} + 2100 q^{38} + 1270 q^{40} - 2240 q^{41} + 1682 q^{42} + 2792 q^{45} - 80 q^{46} + 194 q^{47} - 766 q^{48} - 2760 q^{50} - 20 q^{51} - 7690 q^{52} + 930 q^{53} + 2290 q^{55} + 512 q^{56} - 820 q^{57} - 4272 q^{58} - 934 q^{60} - 20 q^{61} - 90 q^{62} + 350 q^{63} - 4320 q^{66} - 1424 q^{67} - 10440 q^{68} + 3010 q^{70} - 12 q^{71} - 2170 q^{72} - 10 q^{73} + 7272 q^{75} - 10800 q^{77} - 3524 q^{78} + 4158 q^{80} - 51956 q^{81} + 526 q^{82} + 13360 q^{83} - 170 q^{85} - 8364 q^{86} - 4608 q^{88} + 23050 q^{90} - 6288 q^{91} - 4736 q^{92} + 5386 q^{93} + 4020 q^{95} - 29520 q^{96} - 1158 q^{97} + O(q^{100}) \)

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.