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Properties

Label 1078.4.q
Level $1078$
Weight $4$
Character orbit 1078.q
Rep. character $\chi_{1078}(361,\cdot)$
Character field $\Q(\zeta_{15})$
Dimension $960$
Sturm bound $672$

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Defining parameters

Level: \( N \) \(=\) \( 1078 = 2 \cdot 7^{2} \cdot 11 \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 1078.q (of order \(15\) and degree \(8\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 77 \)
Character field: \(\Q(\zeta_{15})\)
Sturm bound: \(672\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{4}(1078, [\chi])\).

Total New Old
Modular forms 4160 960 3200
Cusp forms 3904 960 2944
Eisenstein series 256 0 256

Trace form

\( 960 q + 480 q^{4} - 16 q^{5} - 48 q^{6} + 888 q^{9} + O(q^{10}) \) \( 960 q + 480 q^{4} - 16 q^{5} - 48 q^{6} + 888 q^{9} - 136 q^{10} + 30 q^{11} - 104 q^{13} - 228 q^{15} + 1920 q^{16} + 526 q^{17} - 112 q^{18} + 144 q^{19} + 128 q^{20} - 512 q^{22} - 196 q^{23} + 96 q^{24} + 2924 q^{25} + 32 q^{26} - 72 q^{27} + 2084 q^{29} - 96 q^{30} - 414 q^{31} + 1218 q^{33} - 960 q^{34} - 9664 q^{36} - 852 q^{37} + 248 q^{38} - 2144 q^{39} + 16 q^{40} + 68 q^{41} + 1680 q^{43} - 440 q^{44} - 1344 q^{45} - 472 q^{46} + 376 q^{47} + 448 q^{50} + 272 q^{51} + 208 q^{52} - 840 q^{53} - 3456 q^{54} + 3296 q^{55} + 5360 q^{57} + 1176 q^{58} - 2016 q^{59} - 304 q^{60} - 928 q^{61} - 3808 q^{62} - 15360 q^{64} - 3648 q^{65} - 2528 q^{66} + 3648 q^{67} + 2104 q^{68} + 2456 q^{69} + 6752 q^{71} + 672 q^{72} + 4172 q^{73} + 1568 q^{74} + 5120 q^{75} + 1888 q^{76} + 9920 q^{78} + 6012 q^{79} + 384 q^{80} + 19796 q^{81} - 504 q^{82} + 464 q^{83} + 9416 q^{85} + 548 q^{86} + 16 q^{87} + 464 q^{88} + 1344 q^{89} - 15504 q^{90} - 1792 q^{92} + 168 q^{93} + 2464 q^{94} - 12588 q^{95} + 384 q^{96} + 3852 q^{97} - 9120 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{4}^{\mathrm{new}}(1078, [\chi])\) into newform subspaces

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

Decomposition of \(S_{4}^{\mathrm{old}}(1078, [\chi])\) into lower level spaces

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