# Properties

 Label 3332.2 Level 3332 Weight 2 Dimension 186816 Nonzero newspaces 40 Sturm bound 1354752 Trace bound 5

## Defining parameters

 Level: $$N$$ = $$3332 = 2^{2} \cdot 7^{2} \cdot 17$$ Weight: $$k$$ = $$2$$ Nonzero newspaces: $$40$$ Sturm bound: $$1354752$$ Trace bound: $$5$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{2}(\Gamma_1(3332))$$.

Total New Old
Modular forms 343488 189728 153760
Cusp forms 333889 186816 147073
Eisenstein series 9599 2912 6687

## Trace form

 $$186816 q - 218 q^{2} - 4 q^{3} - 218 q^{4} - 448 q^{5} - 206 q^{6} - 8 q^{7} - 374 q^{8} - 428 q^{9} + O(q^{10})$$ $$186816 q - 218 q^{2} - 4 q^{3} - 218 q^{4} - 448 q^{5} - 206 q^{6} - 8 q^{7} - 374 q^{8} - 428 q^{9} - 182 q^{10} + 4 q^{11} - 158 q^{12} - 404 q^{13} - 228 q^{14} - 162 q^{16} - 480 q^{17} - 442 q^{18} - 4 q^{19} - 206 q^{20} - 482 q^{21} - 434 q^{22} - 20 q^{23} - 238 q^{24} - 392 q^{25} - 222 q^{26} - 16 q^{27} - 300 q^{28} - 704 q^{29} - 166 q^{30} + 60 q^{31} - 178 q^{32} - 328 q^{33} - 163 q^{34} + 30 q^{35} - 262 q^{36} - 296 q^{37} - 94 q^{38} + 106 q^{39} - 94 q^{40} - 284 q^{41} - 222 q^{42} + 60 q^{43} - 102 q^{44} - 190 q^{45} - 142 q^{46} + 80 q^{47} - 272 q^{48} - 356 q^{49} - 636 q^{50} + 46 q^{51} - 454 q^{52} - 432 q^{53} - 294 q^{54} + 122 q^{55} - 228 q^{56} - 744 q^{57} - 286 q^{58} + 32 q^{59} - 358 q^{60} - 350 q^{61} - 262 q^{62} + 36 q^{63} - 374 q^{64} - 296 q^{65} - 318 q^{66} + 44 q^{67} - 315 q^{68} - 804 q^{69} - 234 q^{70} - 370 q^{72} - 220 q^{73} - 302 q^{74} - 262 q^{76} - 450 q^{77} - 586 q^{78} + 36 q^{79} - 444 q^{80} - 400 q^{81} - 408 q^{82} - 72 q^{83} - 708 q^{84} - 830 q^{85} - 740 q^{86} - 312 q^{87} - 532 q^{88} - 400 q^{89} - 924 q^{90} - 184 q^{91} - 568 q^{92} - 832 q^{93} - 608 q^{94} - 276 q^{95} - 864 q^{96} - 744 q^{97} - 864 q^{98} - 80 q^{99} + O(q^{100})$$

## Decomposition of $$S_{2}^{\mathrm{new}}(\Gamma_1(3332))$$

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
3332.2.a $$\chi_{3332}(1, \cdot)$$ 3332.2.a.a 1 1
3332.2.a.b 1
3332.2.a.c 1
3332.2.a.d 1
3332.2.a.e 1
3332.2.a.f 1
3332.2.a.g 2
3332.2.a.h 2
3332.2.a.i 2
3332.2.a.j 2
3332.2.a.k 2
3332.2.a.l 2
3332.2.a.m 2
3332.2.a.n 2
3332.2.a.o 2
3332.2.a.p 3
3332.2.a.q 3
3332.2.a.r 4
3332.2.a.s 4
3332.2.a.t 8
3332.2.a.u 8
3332.2.b $$\chi_{3332}(2549, \cdot)$$ 3332.2.b.a 2 1
3332.2.b.b 8
3332.2.b.c 8
3332.2.b.d 12
3332.2.b.e 12
3332.2.b.f 20
3332.2.e $$\chi_{3332}(3331, \cdot)$$ n/a 352 1
3332.2.f $$\chi_{3332}(783, \cdot)$$ n/a 320 1
3332.2.i $$\chi_{3332}(1157, \cdot)$$ n/a 108 2
3332.2.k $$\chi_{3332}(1959, \cdot)$$ n/a 704 2
3332.2.l $$\chi_{3332}(1177, \cdot)$$ n/a 124 2
3332.2.p $$\chi_{3332}(1599, \cdot)$$ n/a 640 2
3332.2.q $$\chi_{3332}(815, \cdot)$$ n/a 704 2
3332.2.t $$\chi_{3332}(373, \cdot)$$ n/a 120 2
3332.2.u $$\chi_{3332}(477, \cdot)$$ n/a 456 6
3332.2.v $$\chi_{3332}(393, \cdot)$$ n/a 244 4
3332.2.x $$\chi_{3332}(195, \cdot)$$ n/a 1408 4
3332.2.ba $$\chi_{3332}(803, \cdot)$$ n/a 1408 4
3332.2.bb $$\chi_{3332}(361, \cdot)$$ n/a 240 4
3332.2.bf $$\chi_{3332}(307, \cdot)$$ n/a 2688 6
3332.2.bg $$\chi_{3332}(475, \cdot)$$ n/a 3000 6
3332.2.bj $$\chi_{3332}(169, \cdot)$$ n/a 504 6
3332.2.bl $$\chi_{3332}(99, \cdot)$$ n/a 2872 8
3332.2.bm $$\chi_{3332}(97, \cdot)$$ n/a 480 8
3332.2.bo $$\chi_{3332}(137, \cdot)$$ n/a 888 12
3332.2.bq $$\chi_{3332}(569, \cdot)$$ n/a 480 8
3332.2.bs $$\chi_{3332}(19, \cdot)$$ n/a 2816 8
3332.2.bu $$\chi_{3332}(225, \cdot)$$ n/a 1008 12
3332.2.bv $$\chi_{3332}(55, \cdot)$$ n/a 6000 12
3332.2.bx $$\chi_{3332}(305, \cdot)$$ n/a 1008 12
3332.2.ca $$\chi_{3332}(271, \cdot)$$ n/a 6000 12
3332.2.cb $$\chi_{3332}(103, \cdot)$$ n/a 5376 12
3332.2.cf $$\chi_{3332}(129, \cdot)$$ n/a 960 16
3332.2.cg $$\chi_{3332}(79, \cdot)$$ n/a 5632 16
3332.2.cj $$\chi_{3332}(83, \cdot)$$ n/a 12000 24
3332.2.cl $$\chi_{3332}(253, \cdot)$$ n/a 2016 24
3332.2.cn $$\chi_{3332}(81, \cdot)$$ n/a 2016 24
3332.2.co $$\chi_{3332}(47, \cdot)$$ n/a 12000 24
3332.2.cq $$\chi_{3332}(41, \cdot)$$ n/a 4032 48
3332.2.ct $$\chi_{3332}(71, \cdot)$$ n/a 24000 48
3332.2.cu $$\chi_{3332}(59, \cdot)$$ n/a 24000 48
3332.2.cw $$\chi_{3332}(9, \cdot)$$ n/a 4032 48
3332.2.cy $$\chi_{3332}(11, \cdot)$$ n/a 48000 96
3332.2.db $$\chi_{3332}(5, \cdot)$$ n/a 8064 96

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

## Decomposition of $$S_{2}^{\mathrm{old}}(\Gamma_1(3332))$$ into lower level spaces

$$S_{2}^{\mathrm{old}}(\Gamma_1(3332)) \cong$$ $$S_{2}^{\mathrm{new}}(\Gamma_1(14))$$$$^{\oplus 8}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(17))$$$$^{\oplus 9}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(28))$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(34))$$$$^{\oplus 6}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(49))$$$$^{\oplus 6}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(68))$$$$^{\oplus 3}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(98))$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(119))$$$$^{\oplus 6}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(196))$$$$^{\oplus 2}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(238))$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(476))$$$$^{\oplus 2}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(833))$$$$^{\oplus 3}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(1666))$$$$^{\oplus 2}$$