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Properties

Label 1078.2.q
Level $1078$
Weight $2$
Character orbit 1078.q
Rep. character $\chi_{1078}(361,\cdot)$
Character field $\Q(\zeta_{15})$
Dimension $320$
Sturm bound $336$

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Defining parameters

Level: \( N \) \(=\) \( 1078 = 2 \cdot 7^{2} \cdot 11 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1078.q (of order \(15\) and degree \(8\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 77 \)
Character field: \(\Q(\zeta_{15})\)
Sturm bound: \(336\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(1078, [\chi])\).

Total New Old
Modular forms 1472 320 1152
Cusp forms 1216 320 896
Eisenstein series 256 0 256

Trace form

\( 320 q + 40 q^{4} + 4 q^{5} + 8 q^{6} + 64 q^{9} + O(q^{10}) \) \( 320 q + 40 q^{4} + 4 q^{5} + 8 q^{6} + 64 q^{9} + 20 q^{10} - 4 q^{11} + 8 q^{13} - 36 q^{15} + 40 q^{16} - 2 q^{17} + 8 q^{18} - 8 q^{20} + 8 q^{22} + 16 q^{23} - 4 q^{24} + 72 q^{25} - 8 q^{26} + 36 q^{27} + 44 q^{29} - 16 q^{30} - 6 q^{31} - 46 q^{33} + 32 q^{34} - 48 q^{36} + 4 q^{38} + 28 q^{39} - 10 q^{40} + 56 q^{41} - 40 q^{43} - 14 q^{44} - 4 q^{45} - 12 q^{46} + 44 q^{47} - 32 q^{50} - 4 q^{51} - 4 q^{52} + 16 q^{53} + 64 q^{54} + 20 q^{55} + 40 q^{57} - 20 q^{58} + 4 q^{59} - 12 q^{60} + 34 q^{61} - 16 q^{62} - 80 q^{64} - 80 q^{65} - 32 q^{66} - 80 q^{67} - 2 q^{68} - 176 q^{69} - 40 q^{71} - 12 q^{72} + 6 q^{73} - 8 q^{74} - 20 q^{75} - 40 q^{76} - 160 q^{78} - 34 q^{79} - 6 q^{80} - 60 q^{81} - 12 q^{82} - 80 q^{83} + 36 q^{85} - 34 q^{86} - 112 q^{87} - 14 q^{88} - 20 q^{89} - 88 q^{90} + 28 q^{92} - 50 q^{93} - 52 q^{94} + 106 q^{95} - 4 q^{96} - 36 q^{97} + 152 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{2}^{\mathrm{new}}(1078, [\chi])\) into newform subspaces

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

Decomposition of \(S_{2}^{\mathrm{old}}(1078, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(1078, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(77, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(154, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(539, [\chi])\)\(^{\oplus 2}\)