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Properties

Label 368.6
Level 368
Weight 6
Dimension 11741
Nonzero newspaces 8
Sturm bound 50688
Trace bound 5

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Defining parameters

Level: \( N \) = \( 368 = 2^{4} \cdot 23 \)
Weight: \( k \) = \( 6 \)
Nonzero newspaces: \( 8 \)
Sturm bound: \(50688\)
Trace bound: \(5\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{6}(\Gamma_1(368))\).

Total New Old
Modular forms 21428 11929 9499
Cusp forms 20812 11741 9071
Eisenstein series 616 188 428

Trace form

\( 11741 q - 40 q^{2} - 13 q^{3} + 4 q^{4} - 11 q^{5} - 268 q^{6} - 257 q^{7} - 532 q^{8} - 127 q^{9} + O(q^{10}) \) \( 11741 q - 40 q^{2} - 13 q^{3} + 4 q^{4} - 11 q^{5} - 268 q^{6} - 257 q^{7} - 532 q^{8} - 127 q^{9} + 828 q^{10} + 2507 q^{11} - 52 q^{12} - 171 q^{13} + 156 q^{14} - 7881 q^{15} + 1700 q^{16} + 1117 q^{17} + 6232 q^{18} + 12451 q^{19} - 5988 q^{20} - 2175 q^{21} - 8884 q^{22} - 3953 q^{23} - 16824 q^{24} - 4295 q^{25} - 14780 q^{26} - 3697 q^{27} + 14628 q^{28} - 443 q^{29} + 60844 q^{30} + 20095 q^{31} + 47940 q^{32} + 7909 q^{33} + 3436 q^{34} - 23257 q^{35} - 13828 q^{36} + 1189 q^{37} - 106540 q^{38} + 29119 q^{39} - 150588 q^{40} - 16691 q^{41} - 66844 q^{42} - 11845 q^{43} + 80204 q^{44} + 22338 q^{45} + 92488 q^{46} - 43682 q^{47} + 295940 q^{48} + 79309 q^{49} + 170056 q^{50} - 56713 q^{51} - 183188 q^{52} - 111867 q^{53} - 417388 q^{54} + 39935 q^{55} - 382300 q^{56} - 101707 q^{57} - 213596 q^{58} + 77851 q^{59} + 308692 q^{60} + 202549 q^{61} + 547700 q^{62} + 34167 q^{63} + 567508 q^{64} + 60421 q^{65} + 306668 q^{66} + 162947 q^{67} - 267468 q^{68} - 75787 q^{69} - 824408 q^{70} - 157697 q^{71} - 940532 q^{72} - 125363 q^{73} - 294340 q^{74} - 1105455 q^{75} + 174892 q^{76} + 59781 q^{77} + 1263516 q^{78} + 512957 q^{79} + 1108868 q^{80} + 1583701 q^{81} + 186388 q^{82} + 141217 q^{83} - 381820 q^{84} + 122781 q^{85} - 940980 q^{86} - 839559 q^{87} - 1180700 q^{88} - 807979 q^{89} - 560348 q^{90} - 580162 q^{91} + 221852 q^{92} - 1026690 q^{93} + 921780 q^{94} - 482669 q^{95} + 1194612 q^{96} + 126821 q^{97} + 889248 q^{98} + 1537501 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{6}^{\mathrm{new}}(\Gamma_1(368))\)

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 available newforms together with their dimension.

Label \(\chi\) Newforms Dimension \(\chi\) degree
368.6.a \(\chi_{368}(1, \cdot)\) 368.6.a.a 2 1
368.6.a.b 2
368.6.a.c 3
368.6.a.d 3
368.6.a.e 3
368.6.a.f 4
368.6.a.g 4
368.6.a.h 6
368.6.a.i 6
368.6.a.j 7
368.6.a.k 7
368.6.a.l 8
368.6.b \(\chi_{368}(185, \cdot)\) None 0 1
368.6.c \(\chi_{368}(367, \cdot)\) 368.6.c.a 20 1
368.6.c.b 40
368.6.h \(\chi_{368}(183, \cdot)\) None 0 1
368.6.i \(\chi_{368}(91, \cdot)\) n/a 476 2
368.6.j \(\chi_{368}(93, \cdot)\) n/a 440 2
368.6.m \(\chi_{368}(49, \cdot)\) n/a 590 10
368.6.n \(\chi_{368}(7, \cdot)\) None 0 10
368.6.s \(\chi_{368}(15, \cdot)\) n/a 600 10
368.6.t \(\chi_{368}(9, \cdot)\) None 0 10
368.6.w \(\chi_{368}(13, \cdot)\) n/a 4760 20
368.6.x \(\chi_{368}(11, \cdot)\) n/a 4760 20

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

Decomposition of \(S_{6}^{\mathrm{old}}(\Gamma_1(368))\) into lower level spaces

\( S_{6}^{\mathrm{old}}(\Gamma_1(368)) \cong \) \(S_{6}^{\mathrm{new}}(\Gamma_1(4))\)\(^{\oplus 6}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_1(8))\)\(^{\oplus 4}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_1(16))\)\(^{\oplus 2}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_1(23))\)\(^{\oplus 5}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_1(46))\)\(^{\oplus 4}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_1(92))\)\(^{\oplus 3}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_1(184))\)\(^{\oplus 2}\)