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Properties

Label 1078.2.bc
Level $1078$
Weight $2$
Character orbit 1078.bc
Rep. character $\chi_{1078}(9,\cdot)$
Character field $\Q(\zeta_{105})$
Dimension $2688$
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.bc (of order \(105\) and degree \(48\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 539 \)
Character field: \(\Q(\zeta_{105})\)
Sturm bound: \(336\)

Dimensions

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

Total New Old
Modular forms 8256 2688 5568
Cusp forms 7872 2688 5184
Eisenstein series 384 0 384

Trace form

\( 2688 q - 56 q^{4} + 4 q^{5} + 8 q^{6} + 2 q^{7} - 56 q^{9} + O(q^{10}) \) \( 2688 q - 56 q^{4} + 4 q^{5} + 8 q^{6} + 2 q^{7} - 56 q^{9} + 20 q^{10} + 18 q^{11} + 8 q^{13} + 2 q^{14} - 30 q^{15} - 56 q^{16} - 44 q^{17} + 8 q^{18} + 28 q^{19} + 20 q^{20} + 16 q^{21} + 6 q^{22} + 100 q^{23} - 4 q^{24} - 48 q^{25} + 20 q^{26} - 90 q^{27} + 14 q^{28} + 12 q^{29} - 6 q^{31} - 46 q^{33} + 32 q^{34} + 62 q^{35} + 112 q^{36} + 16 q^{37} - 52 q^{38} + 20 q^{39} + 74 q^{40} + 56 q^{41} + 66 q^{42} - 40 q^{43} - 34 q^{44} - 32 q^{45} + 4 q^{46} - 138 q^{47} - 178 q^{49} - 32 q^{50} + 324 q^{51} - 4 q^{52} + 100 q^{53} + 64 q^{54} - 22 q^{55} - 52 q^{56} + 8 q^{57} - 244 q^{58} + 32 q^{59} - 52 q^{60} + 34 q^{61} + 68 q^{62} + 10 q^{63} + 112 q^{64} - 32 q^{65} - 32 q^{66} - 48 q^{67} + 54 q^{68} - 120 q^{69} - 48 q^{70} + 24 q^{71} - 12 q^{72} - 120 q^{73} + 20 q^{74} - 20 q^{75} - 40 q^{76} + 36 q^{77} - 32 q^{78} + 14 q^{79} - 6 q^{80} + 52 q^{81} - 12 q^{82} + 4 q^{83} - 36 q^{84} + 52 q^{85} - 144 q^{86} - 308 q^{87} - 62 q^{88} + 92 q^{89} - 88 q^{90} + 134 q^{91} + 28 q^{92} + 6 q^{93} - 262 q^{94} - 182 q^{95} - 4 q^{96} - 288 q^{97} + 8 q^{98} - 840 q^{99} + O(q^{100}) \)

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

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