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Properties

Label 483.8.q
Level $483$
Weight $8$
Character orbit 483.q
Rep. character $\chi_{483}(64,\cdot)$
Character field $\Q(\zeta_{11})$
Dimension $1680$
Sturm bound $512$

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Defining parameters

Level: \( N \) \(=\) \( 483 = 3 \cdot 7 \cdot 23 \)
Weight: \( k \) \(=\) \( 8 \)
Character orbit: \([\chi]\) \(=\) 483.q (of order \(11\) and degree \(10\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 23 \)
Character field: \(\Q(\zeta_{11})\)
Sturm bound: \(512\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{8}(483, [\chi])\).

Total New Old
Modular forms 4520 1680 2840
Cusp forms 4440 1680 2760
Eisenstein series 80 0 80

Trace form

\( 1680 q + 28 q^{2} - 11012 q^{4} + 216 q^{6} - 1372 q^{7} + 2436 q^{8} - 122472 q^{9} + O(q^{10}) \) \( 1680 q + 28 q^{2} - 11012 q^{4} + 216 q^{6} - 1372 q^{7} + 2436 q^{8} - 122472 q^{9} - 13000 q^{10} - 2864 q^{11} + 9168 q^{13} + 17836 q^{14} + 432 q^{15} - 501812 q^{16} - 59836 q^{17} + 20412 q^{18} - 54588 q^{19} - 227960 q^{20} - 37044 q^{21} + 1310832 q^{22} + 265900 q^{23} + 109512 q^{24} - 2922284 q^{25} - 577832 q^{26} - 215404 q^{28} + 385428 q^{29} - 58752 q^{30} + 1431964 q^{31} + 1749708 q^{32} - 462456 q^{33} - 2715876 q^{34} + 117992 q^{35} - 6568290 q^{36} + 625252 q^{37} - 634624 q^{38} - 4547016 q^{39} - 6748860 q^{40} - 3799984 q^{41} - 296352 q^{42} - 907308 q^{43} + 9940990 q^{44} + 15678120 q^{46} + 6982072 q^{47} + 703728 q^{48} - 19765032 q^{49} - 20847274 q^{50} - 10348020 q^{51} + 6126752 q^{52} - 11564440 q^{53} - 708588 q^{54} + 16536244 q^{55} + 7651644 q^{56} + 9384444 q^{57} + 9836574 q^{58} + 773528 q^{59} - 26929908 q^{60} - 4460128 q^{61} - 21880440 q^{62} - 1000188 q^{63} - 62663340 q^{64} - 821928 q^{65} + 4531680 q^{66} + 17327892 q^{67} + 3986416 q^{68} + 4491288 q^{69} - 3973312 q^{70} + 7924312 q^{71} + 1775844 q^{72} - 14187340 q^{73} - 46979674 q^{74} - 2364336 q^{75} + 36636524 q^{76} + 53615016 q^{77} - 2552256 q^{78} + 25388976 q^{79} - 53426800 q^{80} - 89282088 q^{81} - 136165688 q^{82} - 85774808 q^{83} - 7112448 q^{84} - 10678036 q^{85} - 83992120 q^{86} + 681480 q^{87} + 29719666 q^{88} + 117572976 q^{89} - 9477000 q^{90} + 112852488 q^{91} + 15951096 q^{92} + 26456328 q^{93} + 33283688 q^{94} + 48977648 q^{95} - 64025424 q^{96} - 128935232 q^{97} - 14823774 q^{98} - 2087856 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{8}^{\mathrm{new}}(483, [\chi])\) into newform subspaces

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

Decomposition of \(S_{8}^{\mathrm{old}}(483, [\chi])\) into lower level spaces

\( S_{8}^{\mathrm{old}}(483, [\chi]) \simeq \) \(S_{8}^{\mathrm{new}}(23, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{8}^{\mathrm{new}}(69, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{8}^{\mathrm{new}}(161, [\chi])\)\(^{\oplus 2}\)