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Properties

Label 435.3
Level 435
Weight 3
Dimension 9056
Nonzero newspaces 20
Newform subspaces 30
Sturm bound 40320
Trace bound 5

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Defining parameters

Level: \( N \) = \( 435 = 3 \cdot 5 \cdot 29 \)
Weight: \( k \) = \( 3 \)
Nonzero newspaces: \( 20 \)
Newform subspaces: \( 30 \)
Sturm bound: \(40320\)
Trace bound: \(5\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{3}(\Gamma_1(435))\).

Total New Old
Modular forms 13888 9384 4504
Cusp forms 12992 9056 3936
Eisenstein series 896 328 568

Trace form

\( 9056 q + 8 q^{2} - 20 q^{3} - 40 q^{4} + 8 q^{5} - 68 q^{6} - 40 q^{7} - 24 q^{8} - 60 q^{9} + O(q^{10}) \) \( 9056 q + 8 q^{2} - 20 q^{3} - 40 q^{4} + 8 q^{5} - 68 q^{6} - 40 q^{7} - 24 q^{8} - 60 q^{9} - 132 q^{10} - 32 q^{11} - 84 q^{12} - 56 q^{13} - 10 q^{15} - 72 q^{16} + 80 q^{17} + 76 q^{18} + 40 q^{19} + 408 q^{20} + 308 q^{21} + 536 q^{22} + 168 q^{23} + 500 q^{24} - 28 q^{25} + 104 q^{26} - 32 q^{27} - 112 q^{28} - 112 q^{29} - 164 q^{30} - 408 q^{31} - 744 q^{32} - 336 q^{33} - 880 q^{34} - 312 q^{35} - 1348 q^{36} - 624 q^{37} - 928 q^{38} - 516 q^{39} - 604 q^{40} + 112 q^{41} + 68 q^{42} - 104 q^{43} + 728 q^{44} - 26 q^{45} + 2928 q^{46} + 864 q^{47} + 1740 q^{48} + 1592 q^{49} + 1044 q^{50} + 316 q^{51} + 2408 q^{52} + 896 q^{53} - 60 q^{54} + 652 q^{55} + 392 q^{56} + 128 q^{57} - 576 q^{58} - 224 q^{59} - 634 q^{60} - 1320 q^{61} - 2136 q^{62} - 412 q^{63} - 3472 q^{64} - 784 q^{65} - 2068 q^{66} - 1992 q^{67} - 4104 q^{68} - 844 q^{69} - 2756 q^{70} - 1024 q^{71} - 2908 q^{72} - 2152 q^{73} - 952 q^{74} - 900 q^{75} - 1064 q^{76} - 176 q^{77} - 2380 q^{78} - 1000 q^{79} - 328 q^{80} - 1140 q^{81} - 872 q^{82} + 32 q^{83} - 400 q^{84} - 228 q^{85} + 448 q^{86} + 56 q^{87} - 256 q^{88} + 550 q^{90} + 248 q^{91} - 208 q^{92} + 756 q^{93} + 440 q^{94} - 288 q^{95} + 6136 q^{96} + 4176 q^{97} + 5136 q^{98} + 5216 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{3}^{\mathrm{new}}(\Gamma_1(435))\)

We only show spaces with odd 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
435.3.b \(\chi_{435}(434, \cdot)\) 435.3.b.a 1 1
435.3.b.b 1
435.3.b.c 1
435.3.b.d 1
435.3.b.e 112
435.3.e \(\chi_{435}(146, \cdot)\) 435.3.e.a 76 1
435.3.g \(\chi_{435}(59, \cdot)\) 435.3.g.a 112 1
435.3.h \(\chi_{435}(86, \cdot)\) 435.3.h.a 2 1
435.3.h.b 2
435.3.h.c 76
435.3.i \(\chi_{435}(17, \cdot)\) 435.3.i.a 232 2
435.3.k \(\chi_{435}(244, \cdot)\) 435.3.k.a 4 2
435.3.k.b 116
435.3.n \(\chi_{435}(28, \cdot)\) 435.3.n.a 4 2
435.3.n.b 4
435.3.n.c 4
435.3.n.d 108
435.3.o \(\chi_{435}(88, \cdot)\) 435.3.o.a 112 2
435.3.r \(\chi_{435}(46, \cdot)\) 435.3.r.a 80 2
435.3.t \(\chi_{435}(278, \cdot)\) 435.3.t.a 232 2
435.3.v \(\chi_{435}(71, \cdot)\) 435.3.v.a 480 6
435.3.w \(\chi_{435}(74, \cdot)\) 435.3.w.a 696 6
435.3.y \(\chi_{435}(161, \cdot)\) 435.3.y.a 480 6
435.3.bb \(\chi_{435}(149, \cdot)\) 435.3.bb.a 696 6
435.3.bc \(\chi_{435}(47, \cdot)\) 435.3.bc.a 1392 12
435.3.be \(\chi_{435}(31, \cdot)\) 435.3.be.a 480 12
435.3.bh \(\chi_{435}(7, \cdot)\) 435.3.bh.a 720 12
435.3.bi \(\chi_{435}(13, \cdot)\) 435.3.bi.a 720 12
435.3.bl \(\chi_{435}(19, \cdot)\) 435.3.bl.a 720 12
435.3.bn \(\chi_{435}(2, \cdot)\) 435.3.bn.a 1392 12

Decomposition of \(S_{3}^{\mathrm{old}}(\Gamma_1(435))\) into lower level spaces

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