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Properties

Label 1078.2.j
Level $1078$
Weight $2$
Character orbit 1078.j
Rep. character $\chi_{1078}(155,\cdot)$
Character field $\Q(\zeta_{7})$
Dimension $264$
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.j (of order \(7\) and degree \(6\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 49 \)
Character field: \(\Q(\zeta_{7})\)
Sturm bound: \(336\)

Dimensions

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

Total New Old
Modular forms 1032 264 768
Cusp forms 984 264 720
Eisenstein series 48 0 48

Trace form

\( 264 q + 4 q^{3} - 44 q^{4} + 4 q^{5} - 20 q^{6} + 8 q^{7} - 56 q^{9} + O(q^{10}) \) \( 264 q + 4 q^{3} - 44 q^{4} + 4 q^{5} - 20 q^{6} + 8 q^{7} - 56 q^{9} + 4 q^{12} + 16 q^{13} + 4 q^{14} + 24 q^{15} - 44 q^{16} + 24 q^{17} + 32 q^{19} + 4 q^{20} + 32 q^{21} + 8 q^{24} - 28 q^{25} + 12 q^{26} + 64 q^{27} + 8 q^{28} - 4 q^{29} + 32 q^{30} + 48 q^{31} + 4 q^{33} + 16 q^{34} + 40 q^{35} - 56 q^{36} - 72 q^{37} + 28 q^{38} - 76 q^{39} - 32 q^{41} - 84 q^{42} + 48 q^{43} + 44 q^{45} - 60 q^{46} - 80 q^{47} - 24 q^{48} + 44 q^{49} + 16 q^{50} + 24 q^{51} - 40 q^{52} - 20 q^{53} - 28 q^{54} + 4 q^{56} - 36 q^{57} - 20 q^{58} - 4 q^{59} + 24 q^{60} - 116 q^{61} + 24 q^{62} - 116 q^{63} - 44 q^{64} + 56 q^{65} + 8 q^{66} + 80 q^{67} + 24 q^{68} + 96 q^{69} + 44 q^{70} - 44 q^{71} + 72 q^{73} + 24 q^{74} - 20 q^{75} + 32 q^{76} + 4 q^{77} - 80 q^{78} + 48 q^{79} - 24 q^{80} - 8 q^{81} + 32 q^{82} - 164 q^{83} - 52 q^{84} - 16 q^{85} + 24 q^{86} + 96 q^{87} + 72 q^{89} - 12 q^{90} + 44 q^{91} - 236 q^{93} + 56 q^{94} + 56 q^{95} + 8 q^{96} + 24 q^{97} + 48 q^{98} + O(q^{100}) \)

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

\( S_{2}^{\mathrm{old}}(1078, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(49, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(98, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(539, [\chi])\)\(^{\oplus 2}\)