# Properties

 Label 1672.2 Level 1672 Weight 2 Dimension 46912 Nonzero newspaces 36 Sturm bound 345600 Trace bound 17

## Defining parameters

 Level: $$N$$ = $$1672 = 2^{3} \cdot 11 \cdot 19$$ Weight: $$k$$ = $$2$$ Nonzero newspaces: $$36$$ Sturm bound: $$345600$$ Trace bound: $$17$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{2}(\Gamma_1(1672))$$.

Total New Old
Modular forms 88560 48136 40424
Cusp forms 84241 46912 37329
Eisenstein series 4319 1224 3095

## Trace form

 $$46912 q - 124 q^{2} - 124 q^{3} - 124 q^{4} - 124 q^{6} - 124 q^{7} - 124 q^{8} - 248 q^{9} + O(q^{10})$$ $$46912 q - 124 q^{2} - 124 q^{3} - 124 q^{4} - 124 q^{6} - 124 q^{7} - 124 q^{8} - 248 q^{9} - 124 q^{10} - 142 q^{11} - 284 q^{12} - 124 q^{14} - 104 q^{15} - 124 q^{16} - 228 q^{17} - 124 q^{18} - 119 q^{19} - 268 q^{20} + 40 q^{21} - 142 q^{22} - 264 q^{23} - 124 q^{24} - 208 q^{25} - 124 q^{26} - 76 q^{27} - 124 q^{28} + 56 q^{29} - 184 q^{30} - 68 q^{31} - 144 q^{32} - 260 q^{33} - 364 q^{34} - 112 q^{35} - 284 q^{36} + 36 q^{37} - 184 q^{38} - 280 q^{39} - 264 q^{40} - 272 q^{41} - 344 q^{42} - 132 q^{43} - 282 q^{44} + 48 q^{45} - 264 q^{46} - 148 q^{47} - 344 q^{48} - 272 q^{49} - 264 q^{50} - 216 q^{51} - 224 q^{52} + 40 q^{53} - 392 q^{54} - 162 q^{55} - 364 q^{56} - 243 q^{57} - 288 q^{58} - 54 q^{59} - 296 q^{60} + 4 q^{61} - 304 q^{62} - 248 q^{63} - 412 q^{64} - 276 q^{65} - 286 q^{66} - 420 q^{67} - 376 q^{68} + 80 q^{69} - 416 q^{70} - 192 q^{71} - 564 q^{72} - 430 q^{73} - 312 q^{74} - 502 q^{75} - 414 q^{76} - 34 q^{77} - 404 q^{78} - 536 q^{79} - 192 q^{80} - 460 q^{81} - 464 q^{82} - 422 q^{83} - 316 q^{84} - 120 q^{85} - 256 q^{86} - 560 q^{87} + 34 q^{88} - 736 q^{89} - 132 q^{90} - 488 q^{91} - 144 q^{92} - 96 q^{93} + 44 q^{94} - 142 q^{95} - 128 q^{96} - 206 q^{97} + 96 q^{98} - 179 q^{99} + O(q^{100})$$

## Decomposition of $$S_{2}^{\mathrm{new}}(\Gamma_1(1672))$$

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
1672.2.a $$\chi_{1672}(1, \cdot)$$ 1672.2.a.a 1 1
1672.2.a.b 1
1672.2.a.c 1
1672.2.a.d 2
1672.2.a.e 3
1672.2.a.f 4
1672.2.a.g 5
1672.2.a.h 6
1672.2.a.i 6
1672.2.a.j 6
1672.2.a.k 9
1672.2.c $$\chi_{1672}(683, \cdot)$$ n/a 200 1
1672.2.e $$\chi_{1672}(837, \cdot)$$ n/a 180 1
1672.2.f $$\chi_{1672}(417, \cdot)$$ 1672.2.f.a 2 1
1672.2.f.b 2
1672.2.f.c 28
1672.2.f.d 28
1672.2.h $$\chi_{1672}(1407, \cdot)$$ None 0 1
1672.2.j $$\chi_{1672}(1253, \cdot)$$ n/a 236 1
1672.2.l $$\chi_{1672}(571, \cdot)$$ n/a 216 1
1672.2.o $$\chi_{1672}(1519, \cdot)$$ None 0 1
1672.2.q $$\chi_{1672}(353, \cdot)$$ 1672.2.q.a 2 2
1672.2.q.b 2
1672.2.q.c 2
1672.2.q.d 4
1672.2.q.e 4
1672.2.q.f 18
1672.2.q.g 18
1672.2.q.h 24
1672.2.q.i 26
1672.2.r $$\chi_{1672}(609, \cdot)$$ n/a 216 4
1672.2.s $$\chi_{1672}(639, \cdot)$$ None 0 2
1672.2.w $$\chi_{1672}(373, \cdot)$$ n/a 472 2
1672.2.y $$\chi_{1672}(923, \cdot)$$ n/a 472 2
1672.2.ba $$\chi_{1672}(65, \cdot)$$ n/a 120 2
1672.2.bc $$\chi_{1672}(87, \cdot)$$ None 0 2
1672.2.bd $$\chi_{1672}(331, \cdot)$$ n/a 400 2
1672.2.bf $$\chi_{1672}(45, \cdot)$$ n/a 400 2
1672.2.bh $$\chi_{1672}(177, \cdot)$$ n/a 300 6
1672.2.bj $$\chi_{1672}(455, \cdot)$$ None 0 4
1672.2.bm $$\chi_{1672}(723, \cdot)$$ n/a 864 4
1672.2.bo $$\chi_{1672}(189, \cdot)$$ n/a 944 4
1672.2.bq $$\chi_{1672}(39, \cdot)$$ None 0 4
1672.2.bs $$\chi_{1672}(569, \cdot)$$ n/a 240 4
1672.2.bt $$\chi_{1672}(229, \cdot)$$ n/a 864 4
1672.2.bv $$\chi_{1672}(75, \cdot)$$ n/a 944 4
1672.2.bx $$\chi_{1672}(49, \cdot)$$ n/a 480 8
1672.2.bz $$\chi_{1672}(43, \cdot)$$ n/a 1416 6
1672.2.cb $$\chi_{1672}(309, \cdot)$$ n/a 1200 6
1672.2.ce $$\chi_{1672}(175, \cdot)$$ None 0 6
1672.2.cf $$\chi_{1672}(287, \cdot)$$ None 0 6
1672.2.ci $$\chi_{1672}(21, \cdot)$$ n/a 1416 6
1672.2.ck $$\chi_{1672}(67, \cdot)$$ n/a 1200 6
1672.2.cl $$\chi_{1672}(241, \cdot)$$ n/a 360 6
1672.2.co $$\chi_{1672}(125, \cdot)$$ n/a 1888 8
1672.2.cq $$\chi_{1672}(27, \cdot)$$ n/a 1888 8
1672.2.cr $$\chi_{1672}(7, \cdot)$$ None 0 8
1672.2.ct $$\chi_{1672}(145, \cdot)$$ n/a 480 8
1672.2.cv $$\chi_{1672}(83, \cdot)$$ n/a 1888 8
1672.2.cx $$\chi_{1672}(293, \cdot)$$ n/a 1888 8
1672.2.db $$\chi_{1672}(31, \cdot)$$ None 0 8
1672.2.dc $$\chi_{1672}(9, \cdot)$$ n/a 1440 24
1672.2.de $$\chi_{1672}(41, \cdot)$$ n/a 1440 24
1672.2.df $$\chi_{1672}(3, \cdot)$$ n/a 5664 24
1672.2.dh $$\chi_{1672}(13, \cdot)$$ n/a 5664 24
1672.2.dk $$\chi_{1672}(15, \cdot)$$ None 0 24
1672.2.dl $$\chi_{1672}(63, \cdot)$$ None 0 24
1672.2.do $$\chi_{1672}(5, \cdot)$$ n/a 5664 24
1672.2.dq $$\chi_{1672}(35, \cdot)$$ n/a 5664 24

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

## Decomposition of $$S_{2}^{\mathrm{old}}(\Gamma_1(1672))$$ into lower level spaces

$$S_{2}^{\mathrm{old}}(\Gamma_1(1672)) \cong$$ $$S_{2}^{\mathrm{new}}(\Gamma_1(11))$$$$^{\oplus 8}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(19))$$$$^{\oplus 8}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(22))$$$$^{\oplus 6}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(38))$$$$^{\oplus 6}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(44))$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(76))$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(88))$$$$^{\oplus 2}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(152))$$$$^{\oplus 2}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(209))$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(418))$$$$^{\oplus 3}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(836))$$$$^{\oplus 2}$$