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Properties

Label 342.6
Level 342
Weight 6
Dimension 4249
Nonzero newspaces 16
Sturm bound 38880
Trace bound 4

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Defining parameters

Level: \( N \) = \( 342 = 2 \cdot 3^{2} \cdot 19 \)
Weight: \( k \) = \( 6 \)
Nonzero newspaces: \( 16 \)
Sturm bound: \(38880\)
Trace bound: \(4\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{6}(\Gamma_1(342))\).

Total New Old
Modular forms 16488 4249 12239
Cusp forms 15912 4249 11663
Eisenstein series 576 0 576

Trace form

\( 4249 q + 16 q^{2} - 18 q^{3} + 64 q^{4} + 84 q^{5} + 168 q^{6} + 356 q^{7} - 128 q^{8} - 1158 q^{9} + O(q^{10}) \) \( 4249 q + 16 q^{2} - 18 q^{3} + 64 q^{4} + 84 q^{5} + 168 q^{6} + 356 q^{7} - 128 q^{8} - 1158 q^{9} - 1008 q^{10} + 666 q^{11} + 768 q^{12} - 2416 q^{13} - 904 q^{14} - 5328 q^{15} + 1024 q^{16} - 4290 q^{17} - 5136 q^{18} + 14200 q^{19} + 4512 q^{20} + 22620 q^{21} - 12 q^{22} + 8334 q^{23} - 1152 q^{24} - 50552 q^{25} - 38824 q^{26} - 36288 q^{27} + 14432 q^{28} + 17874 q^{29} + 14976 q^{30} + 13586 q^{31} + 4096 q^{32} + 810 q^{33} + 20184 q^{34} + 5460 q^{35} + 14880 q^{36} - 42322 q^{37} + 14908 q^{38} + 60864 q^{39} - 16128 q^{40} - 2976 q^{41} - 73920 q^{42} - 179008 q^{43} - 126000 q^{44} - 51516 q^{45} + 153552 q^{46} + 280308 q^{47} + 43008 q^{48} + 334068 q^{49} + 403888 q^{50} + 196578 q^{51} + 22496 q^{52} - 120252 q^{53} - 13464 q^{54} - 590760 q^{55} - 289792 q^{56} - 643887 q^{57} - 322896 q^{58} - 648792 q^{59} - 155520 q^{60} + 123962 q^{61} + 10088 q^{62} + 304728 q^{63} - 32768 q^{64} + 1101768 q^{65} + 623808 q^{66} + 379472 q^{67} + 157296 q^{68} + 315972 q^{69} + 107280 q^{70} - 653064 q^{71} - 158208 q^{72} + 641 q^{73} + 130448 q^{74} + 172806 q^{75} - 2192 q^{76} + 257292 q^{77} - 481680 q^{78} - 168586 q^{79} - 144384 q^{80} - 346014 q^{81} - 712656 q^{82} - 813192 q^{83} + 4032 q^{84} - 281808 q^{85} + 439784 q^{86} + 340092 q^{87} + 136320 q^{88} - 167424 q^{89} + 689472 q^{90} + 958768 q^{91} + 563328 q^{92} + 175560 q^{93} + 582672 q^{94} - 1998942 q^{95} - 24576 q^{96} + 78164 q^{97} - 848232 q^{98} + 55782 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{6}^{\mathrm{new}}(\Gamma_1(342))\)

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
342.6.a \(\chi_{342}(1, \cdot)\) 342.6.a.a 1 1
342.6.a.b 1
342.6.a.c 1
342.6.a.d 1
342.6.a.e 1
342.6.a.f 1
342.6.a.g 2
342.6.a.h 2
342.6.a.i 2
342.6.a.j 2
342.6.a.k 3
342.6.a.l 3
342.6.a.m 3
342.6.a.n 3
342.6.a.o 3
342.6.a.p 4
342.6.a.q 4
342.6.b \(\chi_{342}(341, \cdot)\) 342.6.b.a 18 1
342.6.b.b 18
342.6.e \(\chi_{342}(115, \cdot)\) n/a 180 2
342.6.f \(\chi_{342}(7, \cdot)\) n/a 200 2
342.6.g \(\chi_{342}(163, \cdot)\) 342.6.g.a 6 2
342.6.g.b 8
342.6.g.c 8
342.6.g.d 8
342.6.g.e 10
342.6.g.f 10
342.6.g.g 18
342.6.g.h 18
342.6.h \(\chi_{342}(121, \cdot)\) n/a 200 2
342.6.j \(\chi_{342}(65, \cdot)\) n/a 200 2
342.6.n \(\chi_{342}(293, \cdot)\) n/a 200 2
342.6.p \(\chi_{342}(113, \cdot)\) n/a 200 2
342.6.s \(\chi_{342}(107, \cdot)\) 342.6.s.a 36 2
342.6.s.b 36
342.6.u \(\chi_{342}(55, \cdot)\) n/a 246 6
342.6.v \(\chi_{342}(25, \cdot)\) n/a 600 6
342.6.w \(\chi_{342}(43, \cdot)\) n/a 600 6
342.6.x \(\chi_{342}(29, \cdot)\) n/a 600 6
342.6.bb \(\chi_{342}(53, \cdot)\) n/a 192 6
342.6.bf \(\chi_{342}(155, \cdot)\) n/a 600 6

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

Decomposition of \(S_{6}^{\mathrm{old}}(\Gamma_1(342))\) into lower level spaces

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