Properties

Label 363.4.e
Level $363$
Weight $4$
Character orbit 363.e
Rep. character $\chi_{363}(124,\cdot)$
Character field $\Q(\zeta_{5})$
Dimension $216$
Sturm bound $176$

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Defining parameters

Level: \( N \) \(=\) \( 363 = 3 \cdot 11^{2} \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 363.e (of order \(5\) and degree \(4\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 11 \)
Character field: \(\Q(\zeta_{5})\)
Sturm bound: \(176\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{4}(363, [\chi])\).

Total New Old
Modular forms 576 216 360
Cusp forms 480 216 264
Eisenstein series 96 0 96

Trace form

\( 216 q - 4 q^{2} - 196 q^{4} - 16 q^{5} - 12 q^{6} - 52 q^{7} + 116 q^{8} - 486 q^{9} + O(q^{10}) \) \( 216 q - 4 q^{2} - 196 q^{4} - 16 q^{5} - 12 q^{6} - 52 q^{7} + 116 q^{8} - 486 q^{9} + 112 q^{10} - 24 q^{12} - 76 q^{13} - 522 q^{14} - 150 q^{15} - 1384 q^{16} - 148 q^{17} + 54 q^{18} + 8 q^{19} + 394 q^{20} + 336 q^{21} + 928 q^{23} + 126 q^{24} - 1414 q^{25} + 622 q^{26} - 42 q^{28} - 820 q^{29} - 684 q^{30} - 210 q^{31} - 1416 q^{32} - 2512 q^{34} - 240 q^{35} - 1764 q^{36} - 192 q^{37} + 58 q^{38} - 336 q^{39} + 1282 q^{40} + 1460 q^{41} - 192 q^{42} + 360 q^{43} - 144 q^{45} + 1766 q^{46} + 564 q^{47} - 336 q^{48} - 1246 q^{49} + 1578 q^{50} + 216 q^{51} - 1606 q^{52} - 1128 q^{53} + 432 q^{54} - 420 q^{56} + 1044 q^{57} - 222 q^{58} + 332 q^{59} + 360 q^{60} - 1680 q^{61} + 272 q^{62} - 468 q^{63} - 4548 q^{64} - 4240 q^{65} + 2688 q^{67} - 3880 q^{68} - 240 q^{69} + 1140 q^{70} - 716 q^{71} - 1206 q^{72} - 866 q^{73} + 306 q^{74} - 2232 q^{75} + 6048 q^{76} + 96 q^{78} - 84 q^{79} + 2818 q^{80} - 4374 q^{81} - 2774 q^{82} + 7984 q^{83} + 1620 q^{84} + 2340 q^{85} + 6756 q^{86} + 6588 q^{87} + 6120 q^{89} + 828 q^{90} + 1660 q^{91} - 8554 q^{92} + 4812 q^{93} - 4406 q^{94} - 3768 q^{95} - 2334 q^{96} - 1512 q^{97} - 13640 q^{98} + O(q^{100}) \)

Decomposition of \(S_{4}^{\mathrm{new}}(363, [\chi])\) into newform subspaces

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

Decomposition of \(S_{4}^{\mathrm{old}}(363, [\chi])\) into lower level spaces

\( S_{4}^{\mathrm{old}}(363, [\chi]) \cong \) \(S_{4}^{\mathrm{new}}(11, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(33, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(121, [\chi])\)\(^{\oplus 2}\)