Properties

Label 368.4
Level 368
Weight 4
Dimension 7007
Nonzero newspaces 8
Sturm bound 33792
Trace bound 5

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Defining parameters

Level: \( N \) = \( 368 = 2^{4} \cdot 23 \)
Weight: \( k \) = \( 4 \)
Nonzero newspaces: \( 8 \)
Sturm bound: \(33792\)
Trace bound: \(5\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{4}(\Gamma_1(368))\).

Total New Old
Modular forms 12980 7195 5785
Cusp forms 12364 7007 5357
Eisenstein series 616 188 428

Trace form

\( 7007 q - 40 q^{2} - 37 q^{3} - 60 q^{4} - 47 q^{5} + 20 q^{6} + 15 q^{7} + 44 q^{8} + 11 q^{9} + O(q^{10}) \) \( 7007 q - 40 q^{2} - 37 q^{3} - 60 q^{4} - 47 q^{5} + 20 q^{6} + 15 q^{7} + 44 q^{8} + 11 q^{9} + 92 q^{10} - 157 q^{11} - 244 q^{12} - 95 q^{13} - 420 q^{14} + 231 q^{15} - 604 q^{16} - 191 q^{17} - 392 q^{18} + 107 q^{19} + 348 q^{20} + 33 q^{21} + 1132 q^{22} - 89 q^{23} + 1608 q^{24} + 231 q^{25} + 484 q^{26} - 97 q^{27} - 604 q^{28} - 47 q^{29} - 2516 q^{30} - 1089 q^{31} - 1980 q^{32} - 443 q^{33} - 916 q^{34} - 1081 q^{35} + 1148 q^{36} + 289 q^{37} + 2420 q^{38} - 209 q^{39} + 2628 q^{40} + 385 q^{41} + 1316 q^{42} + 1747 q^{43} - 1780 q^{44} - 498 q^{45} - 1176 q^{46} + 2878 q^{47} - 3580 q^{48} - 753 q^{49} - 1496 q^{50} + 2567 q^{51} + 428 q^{52} + 1185 q^{53} + 2708 q^{54} + 143 q^{55} + 932 q^{56} + 341 q^{57} - 60 q^{58} - 4781 q^{59} + 340 q^{60} - 2975 q^{61} + 116 q^{62} - 5817 q^{63} - 1068 q^{64} + 973 q^{65} + 812 q^{66} - 3541 q^{67} + 1716 q^{68} - 859 q^{69} - 408 q^{70} + 1423 q^{71} - 2228 q^{72} - 319 q^{73} + 860 q^{74} - 5103 q^{75} + 2412 q^{76} - 2643 q^{77} + 1500 q^{78} + 3197 q^{79} + 5252 q^{80} - 3785 q^{81} + 1364 q^{82} + 6817 q^{83} - 3964 q^{84} + 6637 q^{85} - 7572 q^{86} + 12441 q^{87} - 3100 q^{88} + 6041 q^{89} - 3836 q^{90} + 6382 q^{91} - 676 q^{92} + 14742 q^{93} + 6452 q^{94} - 3581 q^{95} + 8820 q^{96} + 6233 q^{97} - 672 q^{98} - 2051 q^{99} + O(q^{100}) \)

Decomposition of \(S_{4}^{\mathrm{new}}(\Gamma_1(368))\)

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 the newforms together with their dimension.

Label \(\chi\) Newforms Dimension \(\chi\) degree
368.4.a \(\chi_{368}(1, \cdot)\) 368.4.a.a 1 1
368.4.a.b 1
368.4.a.c 1
368.4.a.d 1
368.4.a.e 1
368.4.a.f 2
368.4.a.g 2
368.4.a.h 3
368.4.a.i 3
368.4.a.j 3
368.4.a.k 3
368.4.a.l 4
368.4.a.m 4
368.4.a.n 4
368.4.b \(\chi_{368}(185, \cdot)\) None 0 1
368.4.c \(\chi_{368}(367, \cdot)\) 368.4.c.a 12 1
368.4.c.b 24
368.4.h \(\chi_{368}(183, \cdot)\) None 0 1
368.4.i \(\chi_{368}(91, \cdot)\) n/a 284 2
368.4.j \(\chi_{368}(93, \cdot)\) n/a 264 2
368.4.m \(\chi_{368}(49, \cdot)\) n/a 350 10
368.4.n \(\chi_{368}(7, \cdot)\) None 0 10
368.4.s \(\chi_{368}(15, \cdot)\) n/a 360 10
368.4.t \(\chi_{368}(9, \cdot)\) None 0 10
368.4.w \(\chi_{368}(13, \cdot)\) n/a 2840 20
368.4.x \(\chi_{368}(11, \cdot)\) n/a 2840 20

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

Decomposition of \(S_{4}^{\mathrm{old}}(\Gamma_1(368))\) into lower level spaces

\( S_{4}^{\mathrm{old}}(\Gamma_1(368)) \cong \) \(S_{4}^{\mathrm{new}}(\Gamma_1(8))\)\(^{\oplus 4}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(16))\)\(^{\oplus 2}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(23))\)\(^{\oplus 5}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(46))\)\(^{\oplus 4}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(92))\)\(^{\oplus 3}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(184))\)\(^{\oplus 2}\)