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Properties

Label 363.6
Level 363
Weight 6
Dimension 17711
Nonzero newspaces 8
Sturm bound 58080
Trace bound 1

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Defining parameters

Level: \( N \) = \( 363 = 3 \cdot 11^{2} \)
Weight: \( k \) = \( 6 \)
Nonzero newspaces: \( 8 \)
Sturm bound: \(58080\)
Trace bound: \(1\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{6}(\Gamma_1(363))\).

Total New Old
Modular forms 24520 17991 6529
Cusp forms 23880 17711 6169
Eisenstein series 640 280 360

Trace form

\( 17711 q - 6 q^{2} - 36 q^{3} - 86 q^{4} + 6 q^{5} - 139 q^{6} + 1050 q^{7} + 808 q^{8} - 1064 q^{9} + O(q^{10}) \) \( 17711 q - 6 q^{2} - 36 q^{3} - 86 q^{4} + 6 q^{5} - 139 q^{6} + 1050 q^{7} + 808 q^{8} - 1064 q^{9} - 4146 q^{10} - 890 q^{11} - 689 q^{12} + 2568 q^{13} - 1740 q^{14} + 7489 q^{15} + 31334 q^{16} + 7902 q^{17} - 8551 q^{18} - 9586 q^{19} - 34076 q^{20} - 18055 q^{21} - 25240 q^{22} - 11600 q^{23} + 2527 q^{24} + 22341 q^{25} + 61072 q^{26} - 19446 q^{27} + 92850 q^{28} + 29878 q^{29} + 23721 q^{30} - 62130 q^{31} - 160520 q^{32} + 6890 q^{33} + 38138 q^{34} + 111680 q^{35} + 115559 q^{36} + 103980 q^{37} + 81436 q^{38} - 41033 q^{39} - 103702 q^{40} - 151470 q^{41} - 298415 q^{42} - 173626 q^{43} - 75790 q^{44} - 71989 q^{45} + 80210 q^{46} + 102548 q^{47} + 200501 q^{48} + 241003 q^{49} + 332914 q^{50} + 313583 q^{51} + 4202 q^{52} + 121970 q^{53} - 62749 q^{54} - 114580 q^{55} - 667920 q^{56} - 609079 q^{57} - 458458 q^{58} + 1056 q^{59} - 20619 q^{60} + 3848 q^{61} + 58560 q^{62} + 332945 q^{63} + 1070182 q^{64} + 571308 q^{65} + 556445 q^{66} + 241142 q^{67} + 279368 q^{68} + 99195 q^{69} - 838150 q^{70} - 673488 q^{71} - 818547 q^{72} - 346060 q^{73} - 5760 q^{74} - 458056 q^{75} - 10174 q^{76} + 259290 q^{77} - 180677 q^{78} + 736690 q^{79} + 80964 q^{80} + 710296 q^{81} + 425250 q^{82} - 375088 q^{83} - 144415 q^{84} - 1376858 q^{85} - 191624 q^{86} - 866593 q^{87} - 1144260 q^{88} - 572726 q^{89} - 819891 q^{90} - 2190630 q^{91} - 1843220 q^{92} - 345445 q^{93} + 941682 q^{94} + 964764 q^{95} + 3260865 q^{96} + 3751952 q^{97} + 5076002 q^{98} + 1119720 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{6}^{\mathrm{new}}(\Gamma_1(363))\)

We only show spaces with even parity, since no modular forms exist when this condition is not satisfied. Within each space \( S_k^{\mathrm{new}}(N, \chi) \) we list available newforms together with their dimension.

Label \(\chi\) Newforms Dimension \(\chi\) degree
363.6.a \(\chi_{363}(1, \cdot)\) 363.6.a.a 1 1
363.6.a.b 1
363.6.a.c 1
363.6.a.d 1
363.6.a.e 1
363.6.a.f 2
363.6.a.g 2
363.6.a.h 2
363.6.a.i 2
363.6.a.j 2
363.6.a.k 3
363.6.a.l 3
363.6.a.m 4
363.6.a.n 4
363.6.a.o 6
363.6.a.p 6
363.6.a.q 10
363.6.a.r 10
363.6.a.s 10
363.6.a.t 10
363.6.a.u 10
363.6.d \(\chi_{363}(362, \cdot)\) n/a 172 1
363.6.e \(\chi_{363}(124, \cdot)\) n/a 360 4
363.6.f \(\chi_{363}(161, \cdot)\) n/a 688 4
363.6.i \(\chi_{363}(34, \cdot)\) n/a 1100 10
363.6.j \(\chi_{363}(32, \cdot)\) n/a 2180 10
363.6.m \(\chi_{363}(4, \cdot)\) n/a 4400 40
363.6.p \(\chi_{363}(2, \cdot)\) n/a 8720 40

"n/a" means that newforms for that character have not been added to the database yet

Decomposition of \(S_{6}^{\mathrm{old}}(\Gamma_1(363))\) into lower level spaces

\( S_{6}^{\mathrm{old}}(\Gamma_1(363)) \cong \) \(S_{6}^{\mathrm{new}}(\Gamma_1(3))\)\(^{\oplus 3}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_1(11))\)\(^{\oplus 4}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_1(33))\)\(^{\oplus 2}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_1(121))\)\(^{\oplus 2}\)