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Properties

Label 1045.2.n
Level $1045$
Weight $2$
Character orbit 1045.n
Rep. character $\chi_{1045}(191,\cdot)$
Character field $\Q(\zeta_{5})$
Dimension $288$
Sturm bound $240$

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Defining parameters

Level: \( N \) \(=\) \( 1045 = 5 \cdot 11 \cdot 19 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1045.n (of order \(5\) and degree \(4\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 11 \)
Character field: \(\Q(\zeta_{5})\)
Sturm bound: \(240\)

Dimensions

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

Total New Old
Modular forms 496 288 208
Cusp forms 464 288 176
Eisenstein series 32 0 32

Trace form

\( 288 q + 8 q^{2} - 64 q^{4} + 8 q^{7} - 16 q^{8} - 84 q^{9} + O(q^{10}) \) \( 288 q + 8 q^{2} - 64 q^{4} + 8 q^{7} - 16 q^{8} - 84 q^{9} - 4 q^{11} - 12 q^{13} - 4 q^{14} - 12 q^{15} - 48 q^{16} + 24 q^{17} - 28 q^{18} + 8 q^{20} + 64 q^{21} - 72 q^{22} + 48 q^{23} - 56 q^{24} - 72 q^{25} - 24 q^{26} - 36 q^{27} + 4 q^{28} + 40 q^{29} + 24 q^{30} + 16 q^{32} + 36 q^{33} + 32 q^{34} + 16 q^{35} - 24 q^{36} - 72 q^{37} - 24 q^{39} - 28 q^{41} - 32 q^{43} + 44 q^{44} + 4 q^{46} - 40 q^{47} - 48 q^{49} + 8 q^{50} - 24 q^{51} + 80 q^{52} - 80 q^{53} - 8 q^{54} - 24 q^{55} - 16 q^{56} + 8 q^{57} + 44 q^{58} + 56 q^{59} - 52 q^{60} - 32 q^{61} + 32 q^{62} - 92 q^{63} + 32 q^{64} + 8 q^{65} - 148 q^{66} + 56 q^{67} - 76 q^{68} + 112 q^{69} + 8 q^{70} - 48 q^{71} - 20 q^{72} - 28 q^{73} - 116 q^{74} + 104 q^{77} + 88 q^{78} - 72 q^{79} - 8 q^{80} - 76 q^{81} + 64 q^{82} + 20 q^{83} - 184 q^{84} + 32 q^{85} + 72 q^{86} + 24 q^{87} - 4 q^{88} + 56 q^{89} - 124 q^{91} - 248 q^{92} + 48 q^{93} - 64 q^{94} + 16 q^{95} + 84 q^{96} - 60 q^{97} + 192 q^{98} - 24 q^{99} + O(q^{100}) \)

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.

Decomposition of \(S_{2}^{\mathrm{old}}(1045, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(1045, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(55, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(209, [\chi])\)\(^{\oplus 2}\)