# Properties

 Label 3675.2 Level 3675 Weight 2 Dimension 310043 Nonzero newspaces 48 Sturm bound 1881600 Trace bound 4

## Defining parameters

 Level: $$N$$ = $$3675 = 3 \cdot 5^{2} \cdot 7^{2}$$ Weight: $$k$$ = $$2$$ Nonzero newspaces: $$48$$ Sturm bound: $$1881600$$ Trace bound: $$4$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{2}(\Gamma_1(3675))$$.

Total New Old
Modular forms 477120 314019 163101
Cusp forms 463681 310043 153638
Eisenstein series 13439 3976 9463

## Trace form

 $$310043q - q^{2} - 206q^{3} - 431q^{4} - 6q^{5} - 356q^{6} - 476q^{7} - 57q^{8} - 222q^{9} + O(q^{10})$$ $$310043q - q^{2} - 206q^{3} - 431q^{4} - 6q^{5} - 356q^{6} - 476q^{7} - 57q^{8} - 222q^{9} - 514q^{10} - 40q^{11} - 240q^{12} - 460q^{13} - 24q^{14} - 446q^{15} - 735q^{16} - 26q^{17} - 202q^{18} - 438q^{19} + 36q^{20} - 385q^{21} - 758q^{22} - 32q^{23} + 6q^{24} - 418q^{25} + 102q^{26} - 74q^{27} - 348q^{28} + 134q^{29} - 82q^{30} - 554q^{31} + 461q^{32} - 7q^{33} - 62q^{34} + 72q^{35} - 182q^{36} - 166q^{37} + 368q^{38} + 72q^{39} - 190q^{40} + 206q^{41} - 21q^{42} - 522q^{43} + 516q^{44} - 104q^{45} - 330q^{46} + 88q^{47} + 285q^{48} - 354q^{49} + 106q^{50} - 543q^{51} + 204q^{52} + 44q^{53} - 86q^{54} - 380q^{55} + 342q^{56} - 159q^{57} + 392q^{58} + 328q^{59} + 14q^{60} - 146q^{61} + 688q^{62} - 204q^{63} + 201q^{64} + 230q^{65} + 125q^{66} + 122q^{67} + 670q^{68} + 79q^{69} - 216q^{70} + 208q^{71} - 24q^{72} + 164q^{73} + 718q^{74} - 162q^{75} - 494q^{76} + 216q^{77} + 107q^{78} + 110q^{79} + 278q^{80} - 282q^{81} + 434q^{82} + 356q^{83} - 4q^{84} - 634q^{85} + 422q^{86} - 143q^{87} + 508q^{88} + 120q^{89} - 456q^{90} - 698q^{91} - 10q^{92} - 233q^{93} - 164q^{94} + 56q^{95} - 777q^{96} - 242q^{97} + 438q^{98} - 880q^{99} + O(q^{100})$$

## Decomposition of $$S_{2}^{\mathrm{new}}(\Gamma_1(3675))$$

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
3675.2.a $$\chi_{3675}(1, \cdot)$$ 3675.2.a.a 1 1
3675.2.a.b 1
3675.2.a.c 1
3675.2.a.d 1
3675.2.a.e 1
3675.2.a.f 1
3675.2.a.g 1
3675.2.a.h 1
3675.2.a.i 1
3675.2.a.j 1
3675.2.a.k 1
3675.2.a.l 1
3675.2.a.m 1
3675.2.a.n 1
3675.2.a.o 1
3675.2.a.p 1
3675.2.a.q 1
3675.2.a.r 2
3675.2.a.s 2
3675.2.a.t 2
3675.2.a.u 2
3675.2.a.v 2
3675.2.a.w 2
3675.2.a.x 2
3675.2.a.y 2
3675.2.a.z 2
3675.2.a.ba 2
3675.2.a.bb 2
3675.2.a.bc 2
3675.2.a.bd 2
3675.2.a.be 2
3675.2.a.bf 2
3675.2.a.bg 2
3675.2.a.bh 2
3675.2.a.bi 3
3675.2.a.bj 3
3675.2.a.bk 4
3675.2.a.bl 4
3675.2.a.bm 4
3675.2.a.bn 4
3675.2.a.bo 4
3675.2.a.bp 4
3675.2.a.bq 4
3675.2.a.br 4
3675.2.a.bs 4
3675.2.a.bt 4
3675.2.a.bu 4
3675.2.a.bv 4
3675.2.a.bw 4
3675.2.a.bx 4
3675.2.a.by 4
3675.2.a.bz 4
3675.2.a.ca 4
3675.2.a.cb 4
3675.2.b $$\chi_{3675}(2351, \cdot)$$ n/a 242 1
3675.2.d $$\chi_{3675}(1324, \cdot)$$ n/a 124 1
3675.2.g $$\chi_{3675}(3674, \cdot)$$ n/a 232 1
3675.2.i $$\chi_{3675}(226, \cdot)$$ n/a 254 2
3675.2.j $$\chi_{3675}(932, \cdot)$$ n/a 472 2
3675.2.m $$\chi_{3675}(832, \cdot)$$ n/a 240 2
3675.2.n $$\chi_{3675}(736, \cdot)$$ n/a 824 4
3675.2.q $$\chi_{3675}(374, \cdot)$$ n/a 464 2
3675.2.r $$\chi_{3675}(949, \cdot)$$ n/a 240 2
3675.2.t $$\chi_{3675}(2126, \cdot)$$ n/a 482 2
3675.2.v $$\chi_{3675}(526, \cdot)$$ n/a 1068 6
3675.2.x $$\chi_{3675}(734, \cdot)$$ n/a 1568 4
3675.2.ba $$\chi_{3675}(589, \cdot)$$ n/a 816 4
3675.2.bc $$\chi_{3675}(146, \cdot)$$ n/a 1568 4
3675.2.bd $$\chi_{3675}(607, \cdot)$$ n/a 480 4
3675.2.bg $$\chi_{3675}(557, \cdot)$$ n/a 928 4
3675.2.bi $$\chi_{3675}(524, \cdot)$$ n/a 1992 6
3675.2.bl $$\chi_{3675}(274, \cdot)$$ n/a 1008 6
3675.2.bn $$\chi_{3675}(251, \cdot)$$ n/a 2088 6
3675.2.bo $$\chi_{3675}(361, \cdot)$$ n/a 1600 8
3675.2.bp $$\chi_{3675}(97, \cdot)$$ n/a 1600 8
3675.2.bs $$\chi_{3675}(197, \cdot)$$ n/a 3200 8
3675.2.bt $$\chi_{3675}(151, \cdot)$$ n/a 2124 12
3675.2.bv $$\chi_{3675}(118, \cdot)$$ n/a 2016 12
3675.2.bw $$\chi_{3675}(218, \cdot)$$ n/a 3984 12
3675.2.bz $$\chi_{3675}(521, \cdot)$$ n/a 3136 8
3675.2.cb $$\chi_{3675}(79, \cdot)$$ n/a 1600 8
3675.2.cc $$\chi_{3675}(509, \cdot)$$ n/a 3136 8
3675.2.cf $$\chi_{3675}(106, \cdot)$$ n/a 6720 24
3675.2.ch $$\chi_{3675}(26, \cdot)$$ n/a 4188 12
3675.2.cj $$\chi_{3675}(424, \cdot)$$ n/a 2016 12
3675.2.ck $$\chi_{3675}(299, \cdot)$$ n/a 3984 12
3675.2.cn $$\chi_{3675}(128, \cdot)$$ n/a 6272 16
3675.2.cq $$\chi_{3675}(178, \cdot)$$ n/a 3200 16
3675.2.cr $$\chi_{3675}(41, \cdot)$$ n/a 13344 24
3675.2.ct $$\chi_{3675}(64, \cdot)$$ n/a 6720 24
3675.2.cw $$\chi_{3675}(104, \cdot)$$ n/a 13344 24
3675.2.cz $$\chi_{3675}(32, \cdot)$$ n/a 7968 24
3675.2.da $$\chi_{3675}(82, \cdot)$$ n/a 4032 24
3675.2.dc $$\chi_{3675}(16, \cdot)$$ n/a 13440 48
3675.2.de $$\chi_{3675}(8, \cdot)$$ n/a 26688 48
3675.2.df $$\chi_{3675}(13, \cdot)$$ n/a 13440 48
3675.2.dj $$\chi_{3675}(59, \cdot)$$ n/a 26688 48
3675.2.dk $$\chi_{3675}(4, \cdot)$$ n/a 13440 48
3675.2.dm $$\chi_{3675}(131, \cdot)$$ n/a 26688 48
3675.2.dp $$\chi_{3675}(52, \cdot)$$ n/a 26880 96
3675.2.dq $$\chi_{3675}(2, \cdot)$$ n/a 53376 96

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

## Decomposition of $$S_{2}^{\mathrm{old}}(\Gamma_1(3675))$$ into lower level spaces

$$S_{2}^{\mathrm{old}}(\Gamma_1(3675)) \cong$$ $$S_{2}^{\mathrm{new}}(\Gamma_1(15))$$$$^{\oplus 6}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(21))$$$$^{\oplus 6}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(25))$$$$^{\oplus 6}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(35))$$$$^{\oplus 8}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(49))$$$$^{\oplus 6}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(75))$$$$^{\oplus 3}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(105))$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(147))$$$$^{\oplus 3}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(175))$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(245))$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(525))$$$$^{\oplus 2}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(735))$$$$^{\oplus 2}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(1225))$$$$^{\oplus 2}$$