↑

Properties

Label 435.4
Level 435
Weight 4
Dimension 13664
Nonzero newspaces 20
Sturm bound 53760
Trace bound 6

Downloads

Learn more

Defining parameters

Level: \( N \) = \( 435 = 3 \cdot 5 \cdot 29 \)
Weight: \( k \) = \( 4 \)
Nonzero newspaces: \( 20 \)
Sturm bound: \(53760\)
Trace bound: \(6\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{4}(\Gamma_1(435))\).

Total New Old
Modular forms 20608 13984 6624
Cusp forms 19712 13664 6048
Eisenstein series 896 320 576

Trace form

\( 13664 q - 8 q^{2} - 16 q^{3} - 8 q^{4} - 12 q^{5} - 84 q^{6} - 16 q^{7} + 72 q^{8} + 8 q^{9} + O(q^{10}) \) \( 13664 q - 8 q^{2} - 16 q^{3} - 8 q^{4} - 12 q^{5} - 84 q^{6} - 16 q^{7} + 72 q^{8} + 8 q^{9} + 108 q^{10} + 112 q^{11} - 244 q^{12} - 384 q^{13} - 528 q^{14} - 390 q^{15} - 776 q^{16} - 80 q^{17} + 380 q^{18} + 456 q^{19} - 976 q^{20} - 476 q^{21} - 584 q^{22} + 464 q^{23} + 1892 q^{24} + 640 q^{25} + 2616 q^{26} + 752 q^{27} + 4768 q^{28} + 2348 q^{29} - 132 q^{30} + 1032 q^{31} + 3352 q^{32} + 668 q^{33} + 800 q^{34} + 256 q^{35} - 3396 q^{36} - 6160 q^{38} - 3372 q^{39} - 4148 q^{40} + 728 q^{41} - 604 q^{42} - 960 q^{43} - 8456 q^{44} - 1680 q^{45} - 21952 q^{46} - 6400 q^{47} - 5860 q^{48} - 3716 q^{49} + 1388 q^{50} + 2484 q^{51} + 11752 q^{52} + 9100 q^{53} + 404 q^{54} + 11388 q^{55} + 21560 q^{56} + 4336 q^{57} + 38192 q^{58} + 5168 q^{59} + 7262 q^{60} + 7680 q^{61} + 13880 q^{62} - 1300 q^{63} + 5056 q^{64} - 1250 q^{65} - 6036 q^{66} - 7696 q^{67} - 21080 q^{68} - 8716 q^{69} - 19140 q^{70} - 12624 q^{71} + 16484 q^{72} - 19716 q^{73} - 5288 q^{74} + 10150 q^{75} + 7672 q^{76} + 3456 q^{77} - 1244 q^{78} + 2984 q^{79} - 2008 q^{80} - 14176 q^{81} - 7880 q^{82} - 2736 q^{83} - 32656 q^{84} - 8268 q^{85} - 8768 q^{86} - 11312 q^{87} - 4480 q^{88} + 1752 q^{89} - 11170 q^{90} - 3352 q^{91} - 2112 q^{92} - 8844 q^{93} - 6888 q^{94} - 6608 q^{95} - 26632 q^{96} - 49516 q^{97} - 54288 q^{98} - 27412 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{4}^{\mathrm{new}}(\Gamma_1(435))\)

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
435.4.a \(\chi_{435}(1, \cdot)\) 435.4.a.a 1 1
435.4.a.b 1
435.4.a.c 1
435.4.a.d 2
435.4.a.e 2
435.4.a.f 5
435.4.a.g 6
435.4.a.h 6
435.4.a.i 7
435.4.a.j 7
435.4.a.k 8
435.4.a.l 10
435.4.c \(\chi_{435}(349, \cdot)\) 435.4.c.a 42 1
435.4.c.b 42
435.4.d \(\chi_{435}(376, \cdot)\) 435.4.d.a 30 1
435.4.d.b 30
435.4.f \(\chi_{435}(289, \cdot)\) 435.4.f.a 2 1
435.4.f.b 2
435.4.f.c 4
435.4.f.d 4
435.4.f.e 38
435.4.f.f 38
435.4.j \(\chi_{435}(133, \cdot)\) n/a 180 2
435.4.l \(\chi_{435}(104, \cdot)\) n/a 352 2
435.4.m \(\chi_{435}(233, \cdot)\) n/a 336 2
435.4.p \(\chi_{435}(173, \cdot)\) n/a 352 2
435.4.q \(\chi_{435}(41, \cdot)\) n/a 240 2
435.4.s \(\chi_{435}(307, \cdot)\) n/a 180 2
435.4.u \(\chi_{435}(16, \cdot)\) n/a 360 6
435.4.x \(\chi_{435}(4, \cdot)\) n/a 528 6
435.4.z \(\chi_{435}(91, \cdot)\) n/a 360 6
435.4.ba \(\chi_{435}(49, \cdot)\) n/a 552 6
435.4.bd \(\chi_{435}(73, \cdot)\) n/a 1080 12
435.4.bf \(\chi_{435}(11, \cdot)\) n/a 1440 12
435.4.bg \(\chi_{435}(38, \cdot)\) n/a 2112 12
435.4.bj \(\chi_{435}(23, \cdot)\) n/a 2112 12
435.4.bk \(\chi_{435}(14, \cdot)\) n/a 2112 12
435.4.bm \(\chi_{435}(37, \cdot)\) n/a 1080 12

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

Decomposition of \(S_{4}^{\mathrm{old}}(\Gamma_1(435))\) into lower level spaces

\( S_{4}^{\mathrm{old}}(\Gamma_1(435)) \cong \) \(S_{4}^{\mathrm{new}}(\Gamma_1(1))\)\(^{\oplus 8}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(3))\)\(^{\oplus 4}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(5))\)\(^{\oplus 4}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(15))\)\(^{\oplus 2}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(29))\)\(^{\oplus 4}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(87))\)\(^{\oplus 2}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(145))\)\(^{\oplus 2}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(435))\)\(^{\oplus 1}\)