↑

Properties

Label 342.10
Level 342
Weight 10
Dimension 7651
Nonzero newspaces 16
Sturm bound 64800
Trace bound 4

Downloads

Learn more

Defining parameters

Level: \( N \) = \( 342 = 2 \cdot 3^{2} \cdot 19 \)
Weight: \( k \) = \( 10 \)
Nonzero newspaces: \( 16 \)
Sturm bound: \(64800\)
Trace bound: \(4\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{10}(\Gamma_1(342))\).

Total New Old
Modular forms 29448 7651 21797
Cusp forms 28872 7651 21221
Eisenstein series 576 0 576

Trace form

\( 7651 q + 32 q^{2} - 150 q^{3} + 2560 q^{4} + 6444 q^{5} + 6048 q^{6} - 15784 q^{7} - 16384 q^{8} - 27114 q^{9} + O(q^{10}) \) \( 7651 q + 32 q^{2} - 150 q^{3} + 2560 q^{4} + 6444 q^{5} + 6048 q^{6} - 15784 q^{7} - 16384 q^{8} - 27114 q^{9} + 33792 q^{10} + 117426 q^{11} - 150528 q^{12} + 1052912 q^{13} + 808288 q^{14} + 2106252 q^{15} + 655360 q^{16} - 3203268 q^{17} - 847680 q^{18} + 3704770 q^{19} + 340992 q^{20} - 1011960 q^{21} - 6754992 q^{22} - 158700 q^{23} - 1941504 q^{24} + 18233578 q^{25} + 72352 q^{26} - 7203168 q^{27} - 1414144 q^{28} - 10460382 q^{29} + 19224576 q^{30} + 43296734 q^{31} + 2097152 q^{32} - 51415902 q^{33} - 34240608 q^{34} - 89386020 q^{35} + 625152 q^{36} + 84040706 q^{37} + 25926896 q^{38} + 122441340 q^{39} + 8650752 q^{40} + 149125428 q^{41} - 12604416 q^{42} - 547616554 q^{43} + 73079040 q^{44} + 190272564 q^{45} - 209328960 q^{46} - 764082570 q^{47} - 37748736 q^{48} + 108649200 q^{49} + 1083174368 q^{50} + 1330510986 q^{51} + 182357504 q^{52} - 601315464 q^{53} - 695197152 q^{54} - 1796971320 q^{55} - 929595392 q^{56} - 884951529 q^{57} - 206596608 q^{58} + 1479719130 q^{59} + 535587840 q^{60} + 2303645834 q^{61} + 1561663456 q^{62} - 426003420 q^{63} - 738197504 q^{64} - 1911014802 q^{65} - 1614405888 q^{66} - 2159236006 q^{67} - 188060928 q^{68} - 569326068 q^{69} + 3336294720 q^{70} + 4849809870 q^{71} - 85032960 q^{72} - 1933645777 q^{73} + 946307968 q^{74} + 3476855106 q^{75} + 207599872 q^{76} + 3363491490 q^{77} - 208914240 q^{78} - 3990559930 q^{79} + 556793856 q^{80} - 2677892706 q^{81} - 993119232 q^{82} + 4734258810 q^{83} + 113574912 q^{84} + 270064872 q^{85} + 2751517216 q^{86} + 989574552 q^{87} - 511991808 q^{88} - 2991214734 q^{89} + 1078244352 q^{90} - 5488270736 q^{91} + 1154807808 q^{92} + 211866204 q^{93} + 3287828928 q^{94} + 9062590248 q^{95} + 100663296 q^{96} + 11986517990 q^{97} - 1685918400 q^{98} - 12511511694 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{10}^{\mathrm{new}}(\Gamma_1(342))\)

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
342.10.a \(\chi_{342}(1, \cdot)\) 342.10.a.a 1 1
342.10.a.b 1
342.10.a.c 3
342.10.a.d 3
342.10.a.e 3
342.10.a.f 3
342.10.a.g 3
342.10.a.h 3
342.10.a.i 4
342.10.a.j 4
342.10.a.k 4
342.10.a.l 4
342.10.a.m 5
342.10.a.n 6
342.10.a.o 6
342.10.a.p 7
342.10.a.q 7
342.10.b \(\chi_{342}(341, \cdot)\) 342.10.b.a 30 1
342.10.b.b 30
342.10.e \(\chi_{342}(115, \cdot)\) n/a 324 2
342.10.f \(\chi_{342}(7, \cdot)\) n/a 360 2
342.10.g \(\chi_{342}(163, \cdot)\) n/a 150 2
342.10.h \(\chi_{342}(121, \cdot)\) n/a 360 2
342.10.j \(\chi_{342}(65, \cdot)\) n/a 360 2
342.10.n \(\chi_{342}(293, \cdot)\) n/a 360 2
342.10.p \(\chi_{342}(113, \cdot)\) n/a 360 2
342.10.s \(\chi_{342}(107, \cdot)\) n/a 120 2
342.10.u \(\chi_{342}(55, \cdot)\) n/a 450 6
342.10.v \(\chi_{342}(25, \cdot)\) n/a 1080 6
342.10.w \(\chi_{342}(43, \cdot)\) n/a 1080 6
342.10.x \(\chi_{342}(29, \cdot)\) n/a 1080 6
342.10.bb \(\chi_{342}(53, \cdot)\) n/a 360 6
342.10.bf \(\chi_{342}(155, \cdot)\) n/a 1080 6

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

Decomposition of \(S_{10}^{\mathrm{old}}(\Gamma_1(342))\) into lower level spaces

\( S_{10}^{\mathrm{old}}(\Gamma_1(342)) \cong \) \(S_{10}^{\mathrm{new}}(\Gamma_1(2))\)\(^{\oplus 6}\)\(\oplus\)\(S_{10}^{\mathrm{new}}(\Gamma_1(3))\)\(^{\oplus 8}\)\(\oplus\)\(S_{10}^{\mathrm{new}}(\Gamma_1(6))\)\(^{\oplus 4}\)\(\oplus\)\(S_{10}^{\mathrm{new}}(\Gamma_1(9))\)\(^{\oplus 4}\)\(\oplus\)\(S_{10}^{\mathrm{new}}(\Gamma_1(18))\)\(^{\oplus 2}\)\(\oplus\)\(S_{10}^{\mathrm{new}}(\Gamma_1(19))\)\(^{\oplus 6}\)\(\oplus\)\(S_{10}^{\mathrm{new}}(\Gamma_1(38))\)\(^{\oplus 3}\)\(\oplus\)\(S_{10}^{\mathrm{new}}(\Gamma_1(57))\)\(^{\oplus 4}\)\(\oplus\)\(S_{10}^{\mathrm{new}}(\Gamma_1(114))\)\(^{\oplus 2}\)\(\oplus\)\(S_{10}^{\mathrm{new}}(\Gamma_1(171))\)\(^{\oplus 2}\)