# Properties

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

# Learn more about

## 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

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

## 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 the 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

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