# Properties

 Label 3626.2 Level 3626 Weight 2 Dimension 128459 Nonzero newspaces 48 Sturm bound 1608768 Trace bound 19

## Defining parameters

 Level: $$N$$ = $$3626 = 2 \cdot 7^{2} \cdot 37$$ Weight: $$k$$ = $$2$$ Nonzero newspaces: $$48$$ Sturm bound: $$1608768$$ Trace bound: $$19$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{2}(\Gamma_1(3626))$$.

Total New Old
Modular forms 406512 128459 278053
Cusp forms 397873 128459 269414
Eisenstein series 8639 0 8639

## Trace form

 $$128459 q - 2 q^{2} + 6 q^{4} + 12 q^{5} + 16 q^{6} + 16 q^{7} - 2 q^{8} + 30 q^{9} + O(q^{10})$$ $$128459 q - 2 q^{2} + 6 q^{4} + 12 q^{5} + 16 q^{6} + 16 q^{7} - 2 q^{8} + 30 q^{9} + 12 q^{10} + 24 q^{11} + 12 q^{13} + 12 q^{14} + 48 q^{15} + 6 q^{16} + 60 q^{17} + 22 q^{18} + 48 q^{19} + 12 q^{20} + 52 q^{21} + 24 q^{22} + 48 q^{23} + 16 q^{24} + 42 q^{25} + 53 q^{26} + 144 q^{27} + 16 q^{28} + 72 q^{29} + 120 q^{30} + 156 q^{31} - 2 q^{32} + 168 q^{33} + 84 q^{34} + 84 q^{35} + 75 q^{36} + 70 q^{37} - 16 q^{38} + 32 q^{39} - 27 q^{40} + 48 q^{41} - 108 q^{42} + 24 q^{43} - 60 q^{44} - 156 q^{45} - 132 q^{46} - 84 q^{47} - 16 q^{48} - 236 q^{49} - 77 q^{50} - 240 q^{51} - 16 q^{52} - 36 q^{53} - 188 q^{54} - 276 q^{55} - 72 q^{56} - 24 q^{57} - 84 q^{58} - 36 q^{59} - 36 q^{60} + 5 q^{61} - 4 q^{62} + 72 q^{63} + 6 q^{64} + 249 q^{65} + 96 q^{66} + 156 q^{67} + 60 q^{68} + 336 q^{69} + 84 q^{70} + 216 q^{71} + 22 q^{72} + 228 q^{73} + 34 q^{74} + 468 q^{75} + 48 q^{76} + 168 q^{77} + 80 q^{78} + 264 q^{79} + 12 q^{80} + 174 q^{81} + 60 q^{82} + 12 q^{83} + 52 q^{84} + 129 q^{85} + 56 q^{86} + 60 q^{87} + 24 q^{88} + 33 q^{89} + 156 q^{90} + 20 q^{91} + 84 q^{92} - 108 q^{93} + 216 q^{94} + 48 q^{95} + 16 q^{96} + 132 q^{97} + 96 q^{98} + 156 q^{99} + O(q^{100})$$

## Decomposition of $$S_{2}^{\mathrm{new}}(\Gamma_1(3626))$$

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
3626.2.a $$\chi_{3626}(1, \cdot)$$ 3626.2.a.a 2 1
3626.2.a.b 2
3626.2.a.c 2
3626.2.a.d 2
3626.2.a.e 2
3626.2.a.f 2
3626.2.a.g 2
3626.2.a.h 2
3626.2.a.i 2
3626.2.a.j 2
3626.2.a.k 2
3626.2.a.l 2
3626.2.a.m 2
3626.2.a.n 2
3626.2.a.o 2
3626.2.a.p 2
3626.2.a.q 2
3626.2.a.r 2
3626.2.a.s 2
3626.2.a.t 2
3626.2.a.u 2
3626.2.a.v 3
3626.2.a.w 3
3626.2.a.x 4
3626.2.a.y 4
3626.2.a.z 4
3626.2.a.ba 4
3626.2.a.bb 4
3626.2.a.bc 5
3626.2.a.bd 6
3626.2.a.be 6
3626.2.a.bf 6
3626.2.a.bg 8
3626.2.a.bh 10
3626.2.a.bi 14
3626.2.d $$\chi_{3626}(295, \cdot)$$ n/a 128 1
3626.2.e $$\chi_{3626}(667, \cdot)$$ n/a 240 2
3626.2.f $$\chi_{3626}(491, \cdot)$$ n/a 258 2
3626.2.g $$\chi_{3626}(655, \cdot)$$ n/a 256 2
3626.2.h $$\chi_{3626}(2431, \cdot)$$ n/a 256 2
3626.2.j $$\chi_{3626}(783, \cdot)$$ n/a 248 2
3626.2.m $$\chi_{3626}(471, \cdot)$$ n/a 256 2
3626.2.n $$\chi_{3626}(961, \cdot)$$ n/a 256 2
3626.2.o $$\chi_{3626}(2157, \cdot)$$ n/a 256 2
3626.2.v $$\chi_{3626}(2321, \cdot)$$ n/a 256 2
3626.2.w $$\chi_{3626}(519, \cdot)$$ n/a 1008 6
3626.2.x $$\chi_{3626}(275, \cdot)$$ n/a 756 6
3626.2.y $$\chi_{3626}(197, \cdot)$$ n/a 786 6
3626.2.z $$\chi_{3626}(1255, \cdot)$$ n/a 756 6
3626.2.bb $$\chi_{3626}(97, \cdot)$$ n/a 496 4
3626.2.bc $$\chi_{3626}(325, \cdot)$$ n/a 512 4
3626.2.bd $$\chi_{3626}(31, \cdot)$$ n/a 512 4
3626.2.bh $$\chi_{3626}(717, \cdot)$$ n/a 512 4
3626.2.bi $$\chi_{3626}(813, \cdot)$$ n/a 1080 6
3626.2.bn $$\chi_{3626}(99, \cdot)$$ n/a 780 6
3626.2.bo $$\chi_{3626}(67, \cdot)$$ n/a 756 6
3626.2.br $$\chi_{3626}(361, \cdot)$$ n/a 756 6
3626.2.bu $$\chi_{3626}(359, \cdot)$$ n/a 2112 12
3626.2.bv $$\chi_{3626}(121, \cdot)$$ n/a 2112 12
3626.2.bw $$\chi_{3626}(211, \cdot)$$ n/a 2160 12
3626.2.bx $$\chi_{3626}(149, \cdot)$$ n/a 2016 12
3626.2.by $$\chi_{3626}(265, \cdot)$$ n/a 2160 12
3626.2.ca $$\chi_{3626}(19, \cdot)$$ n/a 1512 12
3626.2.cc $$\chi_{3626}(129, \cdot)$$ n/a 1512 12
3626.2.cd $$\chi_{3626}(587, \cdot)$$ n/a 1536 12
3626.2.cg $$\chi_{3626}(233, \cdot)$$ n/a 2112 12
3626.2.cn $$\chi_{3626}(85, \cdot)$$ n/a 2160 12
3626.2.co $$\chi_{3626}(221, \cdot)$$ n/a 2112 12
3626.2.cp $$\chi_{3626}(11, \cdot)$$ n/a 2112 12
3626.2.cs $$\chi_{3626}(53, \cdot)$$ n/a 6408 36
3626.2.ct $$\chi_{3626}(9, \cdot)$$ n/a 6408 36
3626.2.cu $$\chi_{3626}(71, \cdot)$$ n/a 6336 36
3626.2.cv $$\chi_{3626}(103, \cdot)$$ n/a 4224 24
3626.2.cz $$\chi_{3626}(327, \cdot)$$ n/a 4224 24
3626.2.da $$\chi_{3626}(45, \cdot)$$ n/a 4224 24
3626.2.db $$\chi_{3626}(125, \cdot)$$ n/a 4320 24
3626.2.df $$\chi_{3626}(25, \cdot)$$ n/a 6408 36
3626.2.di $$\chi_{3626}(141, \cdot)$$ n/a 6336 36
3626.2.dj $$\chi_{3626}(65, \cdot)$$ n/a 6408 36
3626.2.do $$\chi_{3626}(13, \cdot)$$ n/a 12672 72
3626.2.dp $$\chi_{3626}(87, \cdot)$$ n/a 12816 72
3626.2.dr $$\chi_{3626}(5, \cdot)$$ n/a 12816 72

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

## Decomposition of $$S_{2}^{\mathrm{old}}(\Gamma_1(3626))$$ into lower level spaces

$$S_{2}^{\mathrm{old}}(\Gamma_1(3626)) \cong$$ $$S_{2}^{\mathrm{new}}(\Gamma_1(14))$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(37))$$$$^{\oplus 6}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(49))$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(74))$$$$^{\oplus 3}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(98))$$$$^{\oplus 2}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(259))$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(518))$$$$^{\oplus 2}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(1813))$$$$^{\oplus 2}$$