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Properties

Label 1078.2.f
Level $1078$
Weight $2$
Character orbit 1078.f
Rep. character $\chi_{1078}(295,\cdot)$
Character field $\Q(\zeta_{5})$
Dimension $164$
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.f (of order \(5\) and degree \(4\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 11 \)
Character field: \(\Q(\zeta_{5})\)
Sturm bound: \(336\)

Dimensions

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

Total New Old
Modular forms 736 164 572
Cusp forms 608 164 444
Eisenstein series 128 0 128

Trace form

\( 164 q - q^{2} - 4 q^{3} - 41 q^{4} + 2 q^{5} + 5 q^{6} - q^{8} - 57 q^{9} + O(q^{10}) \) \( 164 q - q^{2} - 4 q^{3} - 41 q^{4} + 2 q^{5} + 5 q^{6} - q^{8} - 57 q^{9} - 4 q^{10} + 15 q^{11} + 6 q^{12} - 30 q^{15} - 41 q^{16} - 14 q^{17} + 8 q^{18} + 7 q^{19} + 2 q^{20} + 5 q^{22} + 28 q^{23} + 5 q^{24} - 39 q^{25} - 10 q^{26} - 31 q^{27} + 14 q^{29} + 22 q^{30} - 14 q^{31} + 4 q^{32} - 45 q^{33} - 30 q^{34} - 32 q^{36} + 30 q^{37} + 18 q^{38} + 26 q^{39} - 4 q^{40} - 10 q^{41} + 46 q^{43} + 84 q^{45} + 20 q^{46} - 28 q^{47} - 4 q^{48} + 21 q^{50} - 39 q^{51} + 10 q^{52} + 28 q^{53} - 64 q^{54} + 56 q^{55} + 13 q^{57} - 30 q^{58} + 61 q^{59} + 20 q^{60} - 32 q^{61} + 26 q^{62} - 41 q^{64} - 24 q^{66} - 42 q^{67} - 14 q^{68} + 10 q^{69} - 48 q^{71} - 17 q^{72} - 14 q^{73} - 34 q^{74} - 49 q^{75} - 18 q^{76} - 48 q^{78} + 46 q^{79} - 8 q^{80} - 106 q^{81} - 7 q^{82} - 11 q^{83} - 58 q^{85} + q^{86} - 52 q^{87} - 5 q^{88} + 46 q^{89} + 16 q^{90} - 22 q^{92} + 70 q^{93} - 44 q^{94} + 10 q^{95} + 33 q^{97} - 21 q^{99} + O(q^{100}) \)

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

\( S_{2}^{\mathrm{old}}(1078, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(22, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(77, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(154, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(539, [\chi])\)\(^{\oplus 2}\)