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Properties

Label 3525.2
Level 3525
Weight 2
Dimension 303132
Nonzero newspaces 24
Sturm bound 1766400
Trace bound 4

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Defining parameters

Level: \( N \) = \( 3525 = 3 \cdot 5^{2} \cdot 47 \)
Weight: \( k \) = \( 2 \)
Nonzero newspaces: \( 24 \)
Sturm bound: \(1766400\)
Trace bound: \(4\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_1(3525))\).

Total New Old
Modular forms 446752 306824 139928
Cusp forms 436449 303132 133317
Eisenstein series 10303 3692 6611

Trace form

\( 303132 q + 2 q^{2} - 281 q^{3} - 548 q^{4} + 12 q^{5} - 437 q^{6} - 542 q^{7} + 42 q^{8} - 273 q^{9} + O(q^{10}) \) \( 303132 q + 2 q^{2} - 281 q^{3} - 548 q^{4} + 12 q^{5} - 437 q^{6} - 542 q^{7} + 42 q^{8} - 273 q^{9} - 668 q^{10} + 8 q^{11} - 261 q^{12} - 538 q^{13} + 48 q^{14} - 340 q^{15} - 900 q^{16} + 4 q^{17} - 297 q^{18} - 582 q^{19} - 72 q^{20} - 471 q^{21} - 630 q^{22} - 32 q^{23} - 401 q^{24} - 764 q^{25} + 12 q^{26} - 281 q^{27} - 686 q^{28} - 28 q^{29} - 396 q^{30} - 910 q^{31} - 34 q^{32} - 279 q^{33} - 558 q^{34} + 40 q^{35} - 409 q^{36} - 496 q^{37} + 76 q^{38} - 254 q^{39} - 740 q^{40} + 182 q^{41} - 293 q^{42} - 568 q^{43} + 88 q^{44} - 496 q^{45} - 760 q^{46} + 76 q^{47} - 502 q^{48} - 600 q^{49} - 212 q^{50} - 864 q^{51} - 610 q^{52} - 66 q^{53} - 391 q^{54} - 744 q^{55} + 276 q^{56} - 346 q^{57} - 558 q^{58} - 10 q^{59} - 396 q^{60} - 812 q^{61} - 8 q^{62} - 243 q^{63} - 396 q^{64} + 116 q^{65} - 367 q^{66} - 374 q^{67} + 244 q^{68} - 91 q^{69} - 456 q^{70} + 112 q^{71} + 43 q^{72} - 370 q^{73} + 268 q^{74} - 140 q^{75} - 1546 q^{76} + 284 q^{77} + 75 q^{78} - 214 q^{79} + 308 q^{80} - 361 q^{81} - 92 q^{82} + 148 q^{83} + 189 q^{84} - 812 q^{85} + 376 q^{86} - 179 q^{87} - 174 q^{88} + 40 q^{89} - 320 q^{90} - 530 q^{91} + 350 q^{92} - 320 q^{93} - 218 q^{94} - 112 q^{95} - 227 q^{96} - 730 q^{97} + 224 q^{98} - 199 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_1(3525))\)

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
3525.2.a \(\chi_{3525}(1, \cdot)\) 3525.2.a.a 1 1
3525.2.a.b 1
3525.2.a.c 1
3525.2.a.d 1
3525.2.a.e 1
3525.2.a.f 1
3525.2.a.g 1
3525.2.a.h 1
3525.2.a.i 1
3525.2.a.j 1
3525.2.a.k 1
3525.2.a.l 1
3525.2.a.m 1
3525.2.a.n 1
3525.2.a.o 1
3525.2.a.p 2
3525.2.a.q 2
3525.2.a.r 2
3525.2.a.s 2
3525.2.a.t 4
3525.2.a.u 4
3525.2.a.v 5
3525.2.a.w 6
3525.2.a.x 7
3525.2.a.y 7
3525.2.a.z 7
3525.2.a.ba 7
3525.2.a.bb 7
3525.2.a.bc 7
3525.2.a.bd 8
3525.2.a.be 8
3525.2.a.bf 10
3525.2.a.bg 10
3525.2.a.bh 13
3525.2.a.bi 13
3525.2.c \(\chi_{3525}(424, \cdot)\) n/a 136 1
3525.2.e \(\chi_{3525}(3101, \cdot)\) n/a 298 1
3525.2.g \(\chi_{3525}(3524, \cdot)\) n/a 284 1
3525.2.i \(\chi_{3525}(2443, \cdot)\) n/a 288 2
3525.2.j \(\chi_{3525}(518, \cdot)\) n/a 552 2
3525.2.m \(\chi_{3525}(706, \cdot)\) n/a 912 4
3525.2.n \(\chi_{3525}(704, \cdot)\) n/a 1904 4
3525.2.q \(\chi_{3525}(1129, \cdot)\) n/a 928 4
3525.2.s \(\chi_{3525}(281, \cdot)\) n/a 1904 4
3525.2.w \(\chi_{3525}(377, \cdot)\) n/a 3680 8
3525.2.x \(\chi_{3525}(187, \cdot)\) n/a 1920 8
3525.2.y \(\chi_{3525}(451, \cdot)\) n/a 3344 22
3525.2.ba \(\chi_{3525}(374, \cdot)\) n/a 6248 22
3525.2.bc \(\chi_{3525}(26, \cdot)\) n/a 6556 22
3525.2.be \(\chi_{3525}(49, \cdot)\) n/a 3168 22
3525.2.bi \(\chi_{3525}(32, \cdot)\) n/a 12496 44
3525.2.bj \(\chi_{3525}(43, \cdot)\) n/a 6336 44
3525.2.bk \(\chi_{3525}(16, \cdot)\) n/a 21120 88
3525.2.bm \(\chi_{3525}(11, \cdot)\) n/a 41888 88
3525.2.bo \(\chi_{3525}(4, \cdot)\) n/a 21120 88
3525.2.br \(\chi_{3525}(29, \cdot)\) n/a 41888 88
3525.2.bs \(\chi_{3525}(13, \cdot)\) n/a 42240 176
3525.2.bt \(\chi_{3525}(2, \cdot)\) n/a 83776 176

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

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_1(3525))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_1(3525)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_1(15))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(25))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(47))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(75))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(141))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(235))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(705))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(1175))\)\(^{\oplus 2}\)