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Properties

Label 1078.4.v
Level $1078$
Weight $4$
Character orbit 1078.v
Rep. character $\chi_{1078}(15,\cdot)$
Character field $\Q(\zeta_{35})$
Dimension $4032$
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.v (of order \(35\) and degree \(24\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 539 \)
Character field: \(\Q(\zeta_{35})\)
Sturm bound: \(672\)

Dimensions

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

Total New Old
Modular forms 12192 4032 8160
Cusp forms 12000 4032 7968
Eisenstein series 192 0 192

Trace form

\( 4032 q + 672 q^{4} - 32 q^{5} - 24 q^{6} - 24 q^{7} + 1512 q^{9} + O(q^{10}) \) \( 4032 q + 672 q^{4} - 32 q^{5} - 24 q^{6} - 24 q^{7} + 1512 q^{9} + 208 q^{10} - 168 q^{11} - 52 q^{13} - 52 q^{14} + 630 q^{15} + 2688 q^{16} + 836 q^{17} - 224 q^{18} + 592 q^{19} + 320 q^{20} - 280 q^{21} - 364 q^{22} + 784 q^{23} - 96 q^{24} + 4480 q^{25} - 1000 q^{26} - 180 q^{27} + 104 q^{28} - 420 q^{29} - 828 q^{31} + 3012 q^{33} + 960 q^{34} - 1018 q^{35} + 6048 q^{36} - 840 q^{37} - 1240 q^{38} - 560 q^{39} + 560 q^{40} - 2036 q^{41} + 2484 q^{42} - 1680 q^{43} - 616 q^{44} + 5520 q^{45} + 784 q^{46} + 2076 q^{47} + 5890 q^{49} - 448 q^{50} - 3360 q^{51} - 208 q^{52} - 4816 q^{53} + 3456 q^{54} + 220 q^{55} - 352 q^{56} - 2576 q^{57} - 5880 q^{58} - 4820 q^{59} - 1680 q^{60} - 2324 q^{61} + 1636 q^{62} - 1064 q^{63} + 10752 q^{64} - 6272 q^{65} - 1936 q^{66} + 3584 q^{67} + 1776 q^{68} + 4784 q^{69} + 6780 q^{70} + 1344 q^{72} - 5900 q^{73} - 1960 q^{74} + 10240 q^{75} + 1760 q^{76} + 1910 q^{77} - 448 q^{78} + 4536 q^{79} + 768 q^{80} + 29484 q^{81} + 1728 q^{82} + 5092 q^{83} - 720 q^{84} - 5432 q^{85} + 1260 q^{86} - 15356 q^{87} + 2912 q^{88} - 11904 q^{89} - 5160 q^{90} + 6390 q^{91} + 1792 q^{92} - 9632 q^{93} - 15964 q^{94} + 3192 q^{95} - 384 q^{96} + 7992 q^{97} - 11408 q^{98} - 73024 q^{99} + O(q^{100}) \)

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

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