Properties

Label 363.4.m
Level $363$
Weight $4$
Character orbit 363.m
Rep. character $\chi_{363}(4,\cdot)$
Character field $\Q(\zeta_{55})$
Dimension $2640$
Sturm bound $176$

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Defining parameters

Level: \( N \) \(=\) \( 363 = 3 \cdot 11^{2} \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 363.m (of order \(55\) and degree \(40\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 121 \)
Character field: \(\Q(\zeta_{55})\)
Sturm bound: \(176\)

Dimensions

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

Total New Old
Modular forms 5360 2640 2720
Cusp forms 5200 2640 2560
Eisenstein series 160 0 160

Trace form

\( 2640 q - 4 q^{2} + 284 q^{4} - 16 q^{5} - 12 q^{6} - 52 q^{7} + 116 q^{8} - 5940 q^{9} + O(q^{10}) \) \( 2640 q - 4 q^{2} + 284 q^{4} - 16 q^{5} - 12 q^{6} - 52 q^{7} + 116 q^{8} - 5940 q^{9} - 20 q^{10} - 208 q^{11} - 24 q^{12} + 276 q^{13} + 126 q^{14} - 150 q^{15} + 648 q^{16} - 148 q^{17} + 54 q^{18} + 8 q^{19} + 314 q^{20} + 336 q^{21} + 1466 q^{22} - 1484 q^{23} + 126 q^{24} + 1586 q^{25} + 334 q^{26} - 42 q^{28} - 820 q^{29} - 684 q^{30} + 410 q^{31} - 1416 q^{32} + 66 q^{33} - 464 q^{34} - 240 q^{35} + 2556 q^{36} + 1824 q^{37} - 150 q^{38} - 336 q^{39} + 6562 q^{40} + 1460 q^{41} - 144 q^{42} + 360 q^{43} - 2596 q^{44} - 144 q^{45} + 1766 q^{46} + 508 q^{47} - 336 q^{48} + 6946 q^{49} - 6078 q^{50} + 216 q^{51} - 3784 q^{52} + 5564 q^{53} + 432 q^{54} + 492 q^{55} + 1234 q^{56} + 1044 q^{57} + 56 q^{58} + 1788 q^{59} + 1584 q^{60} - 1680 q^{61} - 6218 q^{62} - 468 q^{63} + 7604 q^{64} - 3184 q^{65} - 1296 q^{66} + 732 q^{67} - 3880 q^{68} - 840 q^{69} - 5516 q^{70} - 4044 q^{71} - 1206 q^{72} - 2978 q^{73} + 306 q^{74} - 1608 q^{75} - 19318 q^{76} + 724 q^{77} + 7974 q^{78} - 7652 q^{79} + 5338 q^{80} - 53460 q^{81} - 1270 q^{82} + 7984 q^{83} + 1620 q^{84} + 2692 q^{85} + 4588 q^{86} + 6588 q^{87} - 12112 q^{88} + 2720 q^{89} - 360 q^{90} - 2040 q^{91} + 1150 q^{92} + 2460 q^{93} + 22346 q^{94} - 3768 q^{95} + 5586 q^{96} - 2280 q^{97} - 5016 q^{98} - 3672 q^{99} + O(q^{100}) \)

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

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