## Defining parameters

 Level: $$N$$ = $$2541 = 3 \cdot 7 \cdot 11^{2}$$ Weight: $$k$$ = $$2$$ Nonzero newspaces: $$32$$ Sturm bound: $$929280$$ Trace bound: $$3$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{2}(\Gamma_1(2541))$$.

Total New Old
Modular forms 236160 165636 70524
Cusp forms 228481 162824 65657
Eisenstein series 7679 2812 4867

## Trace form

 $$162824q - 6q^{2} - 184q^{3} - 372q^{4} - 6q^{5} - 160q^{6} - 436q^{7} + 68q^{8} - 138q^{9} + O(q^{10})$$ $$162824q - 6q^{2} - 184q^{3} - 372q^{4} - 6q^{5} - 160q^{6} - 436q^{7} + 68q^{8} - 138q^{9} - 252q^{10} + 20q^{11} - 264q^{12} - 334q^{13} + 60q^{14} - 382q^{15} - 152q^{16} + 96q^{17} - 126q^{18} - 266q^{19} + 152q^{20} - 179q^{21} - 880q^{22} + 56q^{23} - 92q^{24} - 226q^{25} + 158q^{26} - 238q^{27} - 340q^{28} + 56q^{29} - 172q^{30} - 306q^{31} + 20q^{32} - 220q^{33} - 568q^{34} + 74q^{35} - 446q^{36} - 236q^{37} + 134q^{38} - 94q^{39} - 16q^{40} + 180q^{41} - 167q^{42} - 668q^{43} + 220q^{44} - 166q^{45} + 88q^{46} + 238q^{47} + 80q^{48} - 232q^{49} + 344q^{50} + 16q^{51} + 56q^{52} + 220q^{53} - 126q^{54} - 240q^{55} + 222q^{56} - 466q^{57} - 96q^{58} + 84q^{59} - 476q^{60} - 342q^{61} - 60q^{62} - 421q^{63} - 1100q^{64} - 198q^{65} - 450q^{66} - 790q^{67} - 440q^{68} - 464q^{69} - 906q^{70} - 324q^{71} - 932q^{72} - 464q^{73} - 246q^{74} - 526q^{75} - 1060q^{76} - 90q^{77} - 1166q^{78} - 282q^{79} - 552q^{80} - 630q^{81} - 508q^{82} + 76q^{83} - 825q^{84} - 956q^{85} - 298q^{86} - 256q^{87} - 440q^{88} - 40q^{89} - 424q^{90} - 598q^{91} + 32q^{92} - 96q^{93} - 132q^{94} + 354q^{95} - 460q^{96} + 28q^{97} + 440q^{98} - 440q^{99} + O(q^{100})$$

## Decomposition of $$S_{2}^{\mathrm{new}}(\Gamma_1(2541))$$

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
2541.2.a $$\chi_{2541}(1, \cdot)$$ 2541.2.a.a 1 1
2541.2.a.b 1
2541.2.a.c 1
2541.2.a.d 1
2541.2.a.e 1
2541.2.a.f 1
2541.2.a.g 1
2541.2.a.h 1
2541.2.a.i 1
2541.2.a.j 1
2541.2.a.k 1
2541.2.a.l 1
2541.2.a.m 2
2541.2.a.n 2
2541.2.a.o 2
2541.2.a.p 2
2541.2.a.q 2
2541.2.a.r 2
2541.2.a.s 2
2541.2.a.t 2
2541.2.a.u 2
2541.2.a.v 2
2541.2.a.w 2
2541.2.a.x 2
2541.2.a.y 2
2541.2.a.z 2
2541.2.a.ba 2
2541.2.a.bb 2
2541.2.a.bc 2
2541.2.a.bd 2
2541.2.a.be 2
2541.2.a.bf 2
2541.2.a.bg 3
2541.2.a.bh 3
2541.2.a.bi 3
2541.2.a.bj 3
2541.2.a.bk 4
2541.2.a.bl 4
2541.2.a.bm 4
2541.2.a.bn 4
2541.2.a.bo 4
2541.2.a.bp 4
2541.2.a.bq 10
2541.2.a.br 10
2541.2.c $$\chi_{2541}(1693, \cdot)$$ n/a 144 1
2541.2.e $$\chi_{2541}(1574, \cdot)$$ n/a 272 1
2541.2.g $$\chi_{2541}(1814, \cdot)$$ n/a 216 1
2541.2.i $$\chi_{2541}(1453, \cdot)$$ n/a 290 2
2541.2.j $$\chi_{2541}(148, \cdot)$$ n/a 432 4
2541.2.l $$\chi_{2541}(725, \cdot)$$ n/a 544 2
2541.2.n $$\chi_{2541}(122, \cdot)$$ n/a 546 2
2541.2.p $$\chi_{2541}(241, \cdot)$$ n/a 288 2
2541.2.s $$\chi_{2541}(239, \cdot)$$ n/a 864 4
2541.2.u $$\chi_{2541}(251, \cdot)$$ n/a 1088 4
2541.2.w $$\chi_{2541}(118, \cdot)$$ n/a 576 4
2541.2.y $$\chi_{2541}(232, \cdot)$$ n/a 1320 10
2541.2.z $$\chi_{2541}(130, \cdot)$$ n/a 1152 8
2541.2.bb $$\chi_{2541}(197, \cdot)$$ n/a 2640 10
2541.2.bd $$\chi_{2541}(188, \cdot)$$ n/a 3480 10
2541.2.bf $$\chi_{2541}(76, \cdot)$$ n/a 1760 10
2541.2.bi $$\chi_{2541}(40, \cdot)$$ n/a 1152 8
2541.2.bk $$\chi_{2541}(269, \cdot)$$ n/a 2176 8
2541.2.bm $$\chi_{2541}(233, \cdot)$$ n/a 2176 8
2541.2.bo $$\chi_{2541}(67, \cdot)$$ n/a 3520 20
2541.2.bp $$\chi_{2541}(64, \cdot)$$ n/a 5280 40
2541.2.br $$\chi_{2541}(10, \cdot)$$ n/a 3520 20
2541.2.bt $$\chi_{2541}(89, \cdot)$$ n/a 6960 20
2541.2.bv $$\chi_{2541}(32, \cdot)$$ n/a 6960 20
2541.2.by $$\chi_{2541}(13, \cdot)$$ n/a 7040 40
2541.2.ca $$\chi_{2541}(20, \cdot)$$ n/a 13920 40
2541.2.cc $$\chi_{2541}(8, \cdot)$$ n/a 10560 40
2541.2.ce $$\chi_{2541}(4, \cdot)$$ n/a 14080 80
2541.2.cg $$\chi_{2541}(2, \cdot)$$ n/a 27840 80
2541.2.ci $$\chi_{2541}(5, \cdot)$$ n/a 27840 80
2541.2.ck $$\chi_{2541}(19, \cdot)$$ n/a 14080 80

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

## Decomposition of $$S_{2}^{\mathrm{old}}(\Gamma_1(2541))$$ into lower level spaces

$$S_{2}^{\mathrm{old}}(\Gamma_1(2541)) \cong$$ $$S_{2}^{\mathrm{new}}(\Gamma_1(11))$$$$^{\oplus 8}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(21))$$$$^{\oplus 3}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(33))$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(77))$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(121))$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(231))$$$$^{\oplus 2}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(363))$$$$^{\oplus 2}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(847))$$$$^{\oplus 2}$$