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Properties

Label 1078.4.r
Level $1078$
Weight $4$
Character orbit 1078.r
Rep. character $\chi_{1078}(23,\cdot)$
Character field $\Q(\zeta_{21})$
Dimension $1680$
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.r (of order \(21\) and degree \(12\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 49 \)
Character field: \(\Q(\zeta_{21})\)
Sturm bound: \(672\)

Dimensions

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

Total New Old
Modular forms 6096 1680 4416
Cusp forms 6000 1680 4320
Eisenstein series 96 0 96

Trace form

\( 1680 q + 12 q^{3} + 560 q^{4} + 20 q^{5} - 40 q^{6} - 100 q^{7} + 1484 q^{9} + O(q^{10}) \) \( 1680 q + 12 q^{3} + 560 q^{4} + 20 q^{5} - 40 q^{6} - 100 q^{7} + 1484 q^{9} + 48 q^{12} + 88 q^{13} + 176 q^{14} + 336 q^{15} + 2240 q^{16} - 96 q^{17} - 428 q^{19} - 160 q^{20} + 436 q^{21} - 32 q^{24} + 3500 q^{25} + 312 q^{26} + 744 q^{27} + 128 q^{28} + 588 q^{29} + 112 q^{30} - 472 q^{31} + 132 q^{33} - 304 q^{34} - 200 q^{35} - 9520 q^{36} - 6916 q^{37} + 280 q^{38} - 5796 q^{39} - 1464 q^{41} - 1056 q^{42} - 1120 q^{43} + 1672 q^{45} + 6552 q^{46} + 1336 q^{47} + 2304 q^{48} + 1088 q^{49} - 224 q^{50} + 588 q^{51} + 3632 q^{52} + 1456 q^{53} + 1792 q^{54} - 352 q^{56} + 7224 q^{57} - 2184 q^{58} - 5332 q^{59} - 672 q^{60} - 20488 q^{61} - 1968 q^{62} - 16744 q^{63} - 17920 q^{64} - 1568 q^{65} + 528 q^{66} - 1932 q^{67} - 384 q^{68} + 192 q^{69} + 536 q^{70} + 7672 q^{71} + 244 q^{73} + 840 q^{74} + 9448 q^{75} + 3424 q^{76} - 176 q^{77} - 3360 q^{78} - 1148 q^{79} - 1920 q^{80} + 9632 q^{81} - 400 q^{82} - 8056 q^{83} - 560 q^{84} + 112 q^{85} + 392 q^{86} - 2064 q^{87} + 836 q^{89} + 14088 q^{90} + 3752 q^{91} + 28028 q^{93} - 2352 q^{94} - 532 q^{95} - 128 q^{96} + 1336 q^{97} - 4032 q^{98} + O(q^{100}) \)

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

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