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Properties

Label 1045.2.cf
Level $1045$
Weight $2$
Character orbit 1045.cf
Rep. character $\chi_{1045}(7,\cdot)$
Character field $\Q(\zeta_{60})$
Dimension $1856$
Sturm bound $240$

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Defining parameters

Level: \( N \) \(=\) \( 1045 = 5 \cdot 11 \cdot 19 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1045.cf (of order \(60\) and degree \(16\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 1045 \)
Character field: \(\Q(\zeta_{60})\)
Sturm bound: \(240\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(1045, [\chi])\).

Total New Old
Modular forms 1984 1984 0
Cusp forms 1856 1856 0
Eisenstein series 128 128 0

Trace form

\( 1856 q - 10 q^{2} - 6 q^{3} - 10 q^{5} - 20 q^{6} - 20 q^{7} - 40 q^{8} + O(q^{10}) \) \( 1856 q - 10 q^{2} - 6 q^{3} - 10 q^{5} - 20 q^{6} - 20 q^{7} - 40 q^{8} - 56 q^{11} - 24 q^{12} - 10 q^{13} - 6 q^{15} - 220 q^{16} - 20 q^{17} - 40 q^{18} + 128 q^{20} - 24 q^{22} + 14 q^{25} - 16 q^{26} - 10 q^{28} - 40 q^{30} - 48 q^{31} + 14 q^{33} - 10 q^{35} - 188 q^{36} - 56 q^{37} - 112 q^{38} + 70 q^{40} + 40 q^{41} - 94 q^{42} - 88 q^{45} - 80 q^{46} - 26 q^{47} - 46 q^{48} + 40 q^{50} - 20 q^{51} + 150 q^{52} - 24 q^{53} - 30 q^{55} - 112 q^{56} + 180 q^{57} + 112 q^{58} - 94 q^{60} - 20 q^{61} - 50 q^{62} - 20 q^{63} - 160 q^{68} + 50 q^{70} - 12 q^{71} - 70 q^{72} - 10 q^{73} - 88 q^{75} - 220 q^{77} + 100 q^{78} - 142 q^{80} - 212 q^{81} - 26 q^{82} - 240 q^{83} + 30 q^{85} - 156 q^{86} - 56 q^{88} + 250 q^{90} + 16 q^{91} - 152 q^{92} - 206 q^{93} + 20 q^{95} + 240 q^{96} - 22 q^{97} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{2}^{\mathrm{new}}(1045, [\chi])\) into newform subspaces

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