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Properties

Label 435.2
Level 435
Weight 2
Dimension 4451
Nonzero newspaces 20
Newform subspaces 59
Sturm bound 26880
Trace bound 6

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Defining parameters

Level: \( N \) = \( 435 = 3 \cdot 5 \cdot 29 \)
Weight: \( k \) = \( 2 \)
Nonzero newspaces: \( 20 \)
Newform subspaces: \( 59 \)
Sturm bound: \(26880\)
Trace bound: \(6\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_1(435))\).

Total New Old
Modular forms 7168 4771 2397
Cusp forms 6273 4451 1822
Eisenstein series 895 320 575

Trace form

\( 4451 q + 5 q^{2} - 25 q^{3} - 47 q^{4} - q^{5} - 83 q^{6} - 48 q^{7} + 9 q^{8} - 29 q^{9} + O(q^{10}) \) \( 4451 q + 5 q^{2} - 25 q^{3} - 47 q^{4} - q^{5} - 83 q^{6} - 48 q^{7} + 9 q^{8} - 29 q^{9} - 79 q^{10} + 20 q^{11} - 23 q^{12} - 38 q^{13} + 24 q^{14} - 39 q^{15} - 135 q^{16} + 14 q^{17} - 23 q^{18} - 44 q^{19} - 33 q^{20} - 132 q^{21} - 140 q^{22} - 32 q^{23} - 175 q^{24} - 141 q^{25} - 102 q^{26} - 109 q^{27} - 280 q^{28} - 81 q^{29} - 167 q^{30} - 248 q^{31} - 151 q^{32} - 108 q^{33} - 138 q^{34} - 48 q^{35} - 243 q^{36} - 54 q^{37} - 44 q^{38} - 74 q^{39} - 117 q^{40} + 22 q^{41} - 4 q^{42} - 20 q^{43} + 20 q^{44} - 57 q^{45} - 376 q^{46} - 80 q^{47} - 223 q^{48} - 209 q^{49} - 191 q^{50} - 174 q^{51} - 410 q^{52} - 178 q^{53} - 27 q^{54} - 288 q^{55} - 272 q^{56} - 140 q^{57} - 643 q^{58} - 44 q^{59} - 233 q^{60} - 326 q^{61} - 296 q^{62} - 76 q^{63} - 447 q^{64} - 108 q^{65} - 264 q^{66} - 236 q^{67} - 262 q^{68} - 116 q^{69} - 284 q^{70} - 24 q^{71} + 93 q^{72} - 142 q^{73} + 38 q^{74} + 31 q^{75} - 20 q^{76} + 96 q^{77} + 242 q^{78} + 24 q^{79} + 33 q^{80} + 139 q^{81} + 90 q^{82} + 60 q^{83} + 280 q^{84} - 70 q^{85} + 140 q^{86} + 139 q^{87} + 92 q^{88} + 102 q^{89} + 103 q^{90} - 56 q^{91} + 168 q^{92} + 116 q^{93} + 104 q^{94} + 12 q^{95} + 277 q^{96} - 158 q^{97} - 123 q^{98} - 92 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_1(435))\)

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
435.2.a \(\chi_{435}(1, \cdot)\) 435.2.a.a 1 1
435.2.a.b 1
435.2.a.c 1
435.2.a.d 1
435.2.a.e 2
435.2.a.f 2
435.2.a.g 2
435.2.a.h 2
435.2.a.i 3
435.2.a.j 4
435.2.c \(\chi_{435}(349, \cdot)\) 435.2.c.a 2 1
435.2.c.b 2
435.2.c.c 4
435.2.c.d 10
435.2.c.e 10
435.2.d \(\chi_{435}(376, \cdot)\) 435.2.d.a 10 1
435.2.d.b 10
435.2.f \(\chi_{435}(289, \cdot)\) 435.2.f.a 2 1
435.2.f.b 2
435.2.f.c 2
435.2.f.d 2
435.2.f.e 12
435.2.f.f 12
435.2.j \(\chi_{435}(133, \cdot)\) 435.2.j.a 2 2
435.2.j.b 4
435.2.j.c 24
435.2.j.d 30
435.2.l \(\chi_{435}(104, \cdot)\) 435.2.l.a 112 2
435.2.m \(\chi_{435}(233, \cdot)\) 435.2.m.a 4 2
435.2.m.b 4
435.2.m.c 52
435.2.m.d 52
435.2.p \(\chi_{435}(173, \cdot)\) 435.2.p.a 112 2
435.2.q \(\chi_{435}(41, \cdot)\) 435.2.q.a 4 2
435.2.q.b 4
435.2.q.c 36
435.2.q.d 36
435.2.s \(\chi_{435}(307, \cdot)\) 435.2.s.a 2 2
435.2.s.b 4
435.2.s.c 24
435.2.s.d 30
435.2.u \(\chi_{435}(16, \cdot)\) 435.2.u.a 30 6
435.2.u.b 30
435.2.u.c 30
435.2.u.d 30
435.2.x \(\chi_{435}(4, \cdot)\) 435.2.x.a 96 6
435.2.x.b 96
435.2.z \(\chi_{435}(91, \cdot)\) 435.2.z.a 60 6
435.2.z.b 60
435.2.ba \(\chi_{435}(49, \cdot)\) 435.2.ba.a 168 6
435.2.bd \(\chi_{435}(73, \cdot)\) 435.2.bd.a 180 12
435.2.bd.b 180
435.2.bf \(\chi_{435}(11, \cdot)\) 435.2.bf.a 240 12
435.2.bf.b 240
435.2.bg \(\chi_{435}(38, \cdot)\) 435.2.bg.a 672 12
435.2.bj \(\chi_{435}(23, \cdot)\) 435.2.bj.a 672 12
435.2.bk \(\chi_{435}(14, \cdot)\) 435.2.bk.a 672 12
435.2.bm \(\chi_{435}(37, \cdot)\) 435.2.bm.a 180 12
435.2.bm.b 180

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_1(435))\) into lower level spaces

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