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Properties

Label 342.8
Level 342
Weight 8
Dimension 5953
Nonzero newspaces 16
Sturm bound 51840
Trace bound 4

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Defining parameters

Level: \( N \) = \( 342 = 2 \cdot 3^{2} \cdot 19 \)
Weight: \( k \) = \( 8 \)
Nonzero newspaces: \( 16 \)
Sturm bound: \(51840\)
Trace bound: \(4\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{8}(\Gamma_1(342))\).

Total New Old
Modular forms 22968 5953 17015
Cusp forms 22392 5953 16439
Eisenstein series 576 0 576

Trace form

\( 5953 q - 16 q^{2} + 78 q^{3} + 640 q^{4} - 864 q^{5} - 2544 q^{6} + 788 q^{7} + 2048 q^{8} - 114 q^{9} + O(q^{10}) \) \( 5953 q - 16 q^{2} + 78 q^{3} + 640 q^{4} - 864 q^{5} - 2544 q^{6} + 788 q^{7} + 2048 q^{8} - 114 q^{9} - 1536 q^{10} - 654 q^{11} - 46876 q^{13} - 5072 q^{14} - 36720 q^{15} + 40960 q^{16} + 120990 q^{17} + 6816 q^{18} - 139196 q^{19} - 54144 q^{20} - 555708 q^{21} + 146952 q^{22} + 500478 q^{23} + 15360 q^{24} + 44410 q^{25} - 65168 q^{26} + 401760 q^{27} + 404864 q^{28} - 1932198 q^{29} - 912384 q^{30} - 387094 q^{31} - 65536 q^{32} - 1034946 q^{33} + 518448 q^{34} + 4510548 q^{35} + 670080 q^{36} - 602482 q^{37} - 394408 q^{38} - 4907952 q^{39} - 98304 q^{40} - 3858588 q^{41} + 806400 q^{42} - 3161152 q^{43} + 3005760 q^{44} + 22416156 q^{45} + 13027680 q^{46} + 2375628 q^{47} - 1277952 q^{48} - 19455318 q^{49} - 32879728 q^{50} - 16533486 q^{51} - 1180288 q^{52} + 2323248 q^{53} + 11071440 q^{54} + 31162248 q^{55} + 16052224 q^{56} + 28694139 q^{57} + 12563712 q^{58} + 11954472 q^{59} + 23040 q^{60} - 40613062 q^{61} - 36795152 q^{62} - 31248840 q^{63} - 13107200 q^{64} - 43317432 q^{65} + 4286592 q^{66} + 53198960 q^{67} + 6159936 q^{68} + 37965132 q^{69} + 50593056 q^{70} + 8507064 q^{71} - 18567168 q^{72} - 86222665 q^{73} - 12448448 q^{74} + 44180598 q^{75} - 531776 q^{76} + 30061068 q^{77} + 12030816 q^{78} - 3897082 q^{79} - 884736 q^{80} - 23313402 q^{81} + 16366080 q^{82} + 78879408 q^{83} + 17939712 q^{84} + 44891208 q^{85} + 36414160 q^{86} - 51482772 q^{87} - 10902528 q^{88} - 116934252 q^{89} - 93851136 q^{90} - 43391408 q^{91} - 1546752 q^{92} + 35623800 q^{93} - 33713952 q^{94} - 79758702 q^{95} + 9437184 q^{96} + 168358592 q^{97} + 69271392 q^{98} + 87057990 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{8}^{\mathrm{new}}(\Gamma_1(342))\)

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
342.8.a \(\chi_{342}(1, \cdot)\) 342.8.a.a 1 1
342.8.a.b 1
342.8.a.c 1
342.8.a.d 1
342.8.a.e 1
342.8.a.f 1
342.8.a.g 2
342.8.a.h 2
342.8.a.i 2
342.8.a.j 3
342.8.a.k 3
342.8.a.l 3
342.8.a.m 3
342.8.a.n 3
342.8.a.o 4
342.8.a.p 5
342.8.a.q 5
342.8.a.r 6
342.8.a.s 6
342.8.b \(\chi_{342}(341, \cdot)\) 342.8.b.a 22 1
342.8.b.b 22
342.8.e \(\chi_{342}(115, \cdot)\) n/a 252 2
342.8.f \(\chi_{342}(7, \cdot)\) n/a 280 2
342.8.g \(\chi_{342}(163, \cdot)\) n/a 114 2
342.8.h \(\chi_{342}(121, \cdot)\) n/a 280 2
342.8.j \(\chi_{342}(65, \cdot)\) n/a 280 2
342.8.n \(\chi_{342}(293, \cdot)\) n/a 280 2
342.8.p \(\chi_{342}(113, \cdot)\) n/a 280 2
342.8.s \(\chi_{342}(107, \cdot)\) 342.8.s.a 44 2
342.8.s.b 44
342.8.u \(\chi_{342}(55, \cdot)\) n/a 354 6
342.8.v \(\chi_{342}(25, \cdot)\) n/a 840 6
342.8.w \(\chi_{342}(43, \cdot)\) n/a 840 6
342.8.x \(\chi_{342}(29, \cdot)\) n/a 840 6
342.8.bb \(\chi_{342}(53, \cdot)\) n/a 288 6
342.8.bf \(\chi_{342}(155, \cdot)\) n/a 840 6

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

Decomposition of \(S_{8}^{\mathrm{old}}(\Gamma_1(342))\) into lower level spaces

\( S_{8}^{\mathrm{old}}(\Gamma_1(342)) \cong \) \(S_{8}^{\mathrm{new}}(\Gamma_1(2))\)\(^{\oplus 6}\)\(\oplus\)\(S_{8}^{\mathrm{new}}(\Gamma_1(3))\)\(^{\oplus 8}\)\(\oplus\)\(S_{8}^{\mathrm{new}}(\Gamma_1(6))\)\(^{\oplus 4}\)\(\oplus\)\(S_{8}^{\mathrm{new}}(\Gamma_1(9))\)\(^{\oplus 4}\)\(\oplus\)\(S_{8}^{\mathrm{new}}(\Gamma_1(18))\)\(^{\oplus 2}\)\(\oplus\)\(S_{8}^{\mathrm{new}}(\Gamma_1(19))\)\(^{\oplus 6}\)\(\oplus\)\(S_{8}^{\mathrm{new}}(\Gamma_1(38))\)\(^{\oplus 3}\)\(\oplus\)\(S_{8}^{\mathrm{new}}(\Gamma_1(57))\)\(^{\oplus 4}\)\(\oplus\)\(S_{8}^{\mathrm{new}}(\Gamma_1(114))\)\(^{\oplus 2}\)\(\oplus\)\(S_{8}^{\mathrm{new}}(\Gamma_1(171))\)\(^{\oplus 2}\)