# Properties

 Label 1925.2 Level 1925 Weight 2 Dimension 123222 Nonzero newspaces 84 Sturm bound 576000 Trace bound 12

## Defining parameters

 Level: $$N$$ = $$1925 = 5^{2} \cdot 7 \cdot 11$$ Weight: $$k$$ = $$2$$ Nonzero newspaces: $$84$$ Sturm bound: $$576000$$ Trace bound: $$12$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{2}(\Gamma_1(1925))$$.

Total New Old
Modular forms 147360 126914 20446
Cusp forms 140641 123222 17419
Eisenstein series 6719 3692 3027

## Trace form

 $$123222 q - 210 q^{2} - 204 q^{3} - 186 q^{4} - 244 q^{5} - 290 q^{6} - 238 q^{7} - 436 q^{8} - 130 q^{9} + O(q^{10})$$ $$123222 q - 210 q^{2} - 204 q^{3} - 186 q^{4} - 244 q^{5} - 290 q^{6} - 238 q^{7} - 436 q^{8} - 130 q^{9} - 204 q^{10} - 350 q^{11} - 280 q^{12} - 134 q^{13} - 168 q^{14} - 568 q^{15} - 190 q^{16} - 130 q^{17} - 34 q^{18} - 158 q^{19} - 264 q^{20} - 336 q^{21} - 510 q^{22} - 394 q^{23} - 230 q^{24} - 308 q^{25} - 526 q^{26} - 192 q^{27} - 320 q^{28} - 492 q^{29} - 328 q^{30} - 316 q^{31} - 178 q^{32} - 180 q^{33} - 424 q^{34} - 336 q^{35} - 764 q^{36} - 104 q^{37} - 70 q^{38} - 182 q^{39} - 468 q^{40} - 206 q^{41} - 386 q^{42} - 608 q^{43} - 408 q^{44} - 836 q^{45} - 466 q^{46} - 318 q^{47} - 782 q^{48} - 260 q^{49} - 868 q^{50} - 690 q^{51} - 742 q^{52} - 214 q^{53} - 786 q^{54} - 436 q^{55} - 1102 q^{56} - 748 q^{57} - 822 q^{58} - 400 q^{59} - 824 q^{60} - 708 q^{61} - 694 q^{62} - 642 q^{63} - 1300 q^{64} - 468 q^{65} - 778 q^{66} - 794 q^{67} - 826 q^{68} - 494 q^{69} - 644 q^{70} - 782 q^{71} - 1014 q^{72} - 288 q^{73} - 402 q^{74} - 376 q^{75} - 936 q^{76} - 348 q^{77} - 1224 q^{78} - 212 q^{79} - 516 q^{80} - 248 q^{81} - 342 q^{82} - 276 q^{83} - 810 q^{84} - 844 q^{85} - 298 q^{86} - 188 q^{87} - 300 q^{88} - 618 q^{89} - 1020 q^{90} - 468 q^{91} - 864 q^{92} - 626 q^{93} - 698 q^{94} - 536 q^{95} - 1262 q^{96} - 768 q^{97} - 890 q^{98} - 1102 q^{99} + O(q^{100})$$

## Decomposition of $$S_{2}^{\mathrm{new}}(\Gamma_1(1925))$$

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
1925.2.a $$\chi_{1925}(1, \cdot)$$ 1925.2.a.a 1 1
1925.2.a.b 1
1925.2.a.c 1
1925.2.a.d 1
1925.2.a.e 1
1925.2.a.f 1
1925.2.a.g 1
1925.2.a.h 1
1925.2.a.i 1
1925.2.a.j 1
1925.2.a.k 1
1925.2.a.l 1
1925.2.a.m 1
1925.2.a.n 2
1925.2.a.o 2
1925.2.a.p 2
1925.2.a.q 2
1925.2.a.r 2
1925.2.a.s 2
1925.2.a.t 2
1925.2.a.u 3
1925.2.a.v 3
1925.2.a.w 3
1925.2.a.x 4
1925.2.a.y 6
1925.2.a.z 6
1925.2.a.ba 7
1925.2.a.bb 7
1925.2.a.bc 7
1925.2.a.bd 7
1925.2.a.be 8
1925.2.a.bf 8
1925.2.b $$\chi_{1925}(1849, \cdot)$$ 1925.2.b.a 2 1
1925.2.b.b 2
1925.2.b.c 2
1925.2.b.d 2
1925.2.b.e 2
1925.2.b.f 2
1925.2.b.g 2
1925.2.b.h 4
1925.2.b.i 4
1925.2.b.j 4
1925.2.b.k 4
1925.2.b.l 4
1925.2.b.m 6
1925.2.b.n 6
1925.2.b.o 6
1925.2.b.p 8
1925.2.b.q 14
1925.2.b.r 14
1925.2.c $$\chi_{1925}(76, \cdot)$$ n/a 146 1
1925.2.h $$\chi_{1925}(1924, \cdot)$$ n/a 140 1
1925.2.i $$\chi_{1925}(1101, \cdot)$$ n/a 252 2
1925.2.j $$\chi_{1925}(1343, \cdot)$$ n/a 240 2
1925.2.k $$\chi_{1925}(43, \cdot)$$ n/a 216 2
1925.2.n $$\chi_{1925}(246, \cdot)$$ n/a 720 4
1925.2.o $$\chi_{1925}(386, \cdot)$$ n/a 592 4
1925.2.p $$\chi_{1925}(526, \cdot)$$ n/a 456 4
1925.2.q $$\chi_{1925}(141, \cdot)$$ n/a 720 4
1925.2.r $$\chi_{1925}(36, \cdot)$$ n/a 720 4
1925.2.s $$\chi_{1925}(71, \cdot)$$ n/a 720 4
1925.2.t $$\chi_{1925}(549, \cdot)$$ n/a 280 2
1925.2.y $$\chi_{1925}(1024, \cdot)$$ n/a 240 2
1925.2.z $$\chi_{1925}(626, \cdot)$$ n/a 292 2
1925.2.bc $$\chi_{1925}(41, \cdot)$$ n/a 944 4
1925.2.bd $$\chi_{1925}(379, \cdot)$$ n/a 720 4
1925.2.bg $$\chi_{1925}(1014, \cdot)$$ n/a 944 4
1925.2.bh $$\chi_{1925}(384, \cdot)$$ n/a 944 4
1925.2.bi $$\chi_{1925}(349, \cdot)$$ n/a 560 4
1925.2.bj $$\chi_{1925}(314, \cdot)$$ n/a 944 4
1925.2.bs $$\chi_{1925}(629, \cdot)$$ n/a 944 4
1925.2.bt $$\chi_{1925}(1114, \cdot)$$ n/a 720 4
1925.2.bu $$\chi_{1925}(6, \cdot)$$ n/a 944 4
1925.2.cd $$\chi_{1925}(426, \cdot)$$ n/a 584 4
1925.2.ce $$\chi_{1925}(449, \cdot)$$ n/a 432 4
1925.2.cf $$\chi_{1925}(461, \cdot)$$ n/a 944 4
1925.2.cg $$\chi_{1925}(391, \cdot)$$ n/a 944 4
1925.2.ch $$\chi_{1925}(309, \cdot)$$ n/a 608 4
1925.2.ci $$\chi_{1925}(64, \cdot)$$ n/a 720 4
1925.2.cj $$\chi_{1925}(1091, \cdot)$$ n/a 944 4
1925.2.ck $$\chi_{1925}(169, \cdot)$$ n/a 720 4
1925.2.cn $$\chi_{1925}(139, \cdot)$$ n/a 944 4
1925.2.cq $$\chi_{1925}(32, \cdot)$$ n/a 560 4
1925.2.cr $$\chi_{1925}(243, \cdot)$$ n/a 480 4
1925.2.cu $$\chi_{1925}(366, \cdot)$$ n/a 1888 8
1925.2.cv $$\chi_{1925}(191, \cdot)$$ n/a 1888 8
1925.2.cw $$\chi_{1925}(401, \cdot)$$ n/a 1168 8
1925.2.cx $$\chi_{1925}(221, \cdot)$$ n/a 1600 8
1925.2.cy $$\chi_{1925}(16, \cdot)$$ n/a 1888 8
1925.2.cz $$\chi_{1925}(81, \cdot)$$ n/a 1888 8
1925.2.dc $$\chi_{1925}(162, \cdot)$$ n/a 1440 8
1925.2.dd $$\chi_{1925}(48, \cdot)$$ n/a 1888 8
1925.2.de $$\chi_{1925}(127, \cdot)$$ n/a 1440 8
1925.2.df $$\chi_{1925}(27, \cdot)$$ n/a 1888 8
1925.2.do $$\chi_{1925}(337, \cdot)$$ n/a 1440 8
1925.2.dp $$\chi_{1925}(97, \cdot)$$ n/a 1888 8
1925.2.dq $$\chi_{1925}(57, \cdot)$$ n/a 864 8
1925.2.dr $$\chi_{1925}(8, \cdot)$$ n/a 1440 8
1925.2.ds $$\chi_{1925}(412, \cdot)$$ n/a 1888 8
1925.2.dt $$\chi_{1925}(482, \cdot)$$ n/a 1120 8
1925.2.du $$\chi_{1925}(188, \cdot)$$ n/a 1600 8
1925.2.dv $$\chi_{1925}(197, \cdot)$$ n/a 1440 8
1925.2.ea $$\chi_{1925}(479, \cdot)$$ n/a 1888 8
1925.2.ed $$\chi_{1925}(206, \cdot)$$ n/a 1888 8
1925.2.ee $$\chi_{1925}(131, \cdot)$$ n/a 1888 8
1925.2.ef $$\chi_{1925}(4, \cdot)$$ n/a 1888 8
1925.2.eg $$\chi_{1925}(144, \cdot)$$ n/a 1600 8
1925.2.eh $$\chi_{1925}(101, \cdot)$$ n/a 1168 8
1925.2.ei $$\chi_{1925}(324, \cdot)$$ n/a 1120 8
1925.2.ej $$\chi_{1925}(61, \cdot)$$ n/a 1888 8
1925.2.ek $$\chi_{1925}(9, \cdot)$$ n/a 1888 8
1925.2.et $$\chi_{1925}(289, \cdot)$$ n/a 1888 8
1925.2.eu $$\chi_{1925}(556, \cdot)$$ n/a 1888 8
1925.2.ev $$\chi_{1925}(94, \cdot)$$ n/a 1888 8
1925.2.fe $$\chi_{1925}(24, \cdot)$$ n/a 1120 8
1925.2.ff $$\chi_{1925}(54, \cdot)$$ n/a 1888 8
1925.2.fg $$\chi_{1925}(19, \cdot)$$ n/a 1888 8
1925.2.fh $$\chi_{1925}(129, \cdot)$$ n/a 1888 8
1925.2.fk $$\chi_{1925}(171, \cdot)$$ n/a 1888 8
1925.2.fl $$\chi_{1925}(114, \cdot)$$ n/a 1888 8
1925.2.fo $$\chi_{1925}(3, \cdot)$$ n/a 3776 16
1925.2.fp $$\chi_{1925}(228, \cdot)$$ n/a 3776 16
1925.2.fy $$\chi_{1925}(142, \cdot)$$ n/a 3776 16
1925.2.fz $$\chi_{1925}(12, \cdot)$$ n/a 3200 16
1925.2.ga $$\chi_{1925}(82, \cdot)$$ n/a 2240 16
1925.2.gb $$\chi_{1925}(38, \cdot)$$ n/a 3776 16
1925.2.gc $$\chi_{1925}(2, \cdot)$$ n/a 3776 16
1925.2.gd $$\chi_{1925}(18, \cdot)$$ n/a 2240 16
1925.2.ge $$\chi_{1925}(192, \cdot)$$ n/a 3776 16
1925.2.gf $$\chi_{1925}(513, \cdot)$$ n/a 3776 16
1925.2.gk $$\chi_{1925}(108, \cdot)$$ n/a 3776 16
1925.2.gl $$\chi_{1925}(72, \cdot)$$ n/a 3776 16

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

## Decomposition of $$S_{2}^{\mathrm{old}}(\Gamma_1(1925))$$ into lower level spaces

$$S_{2}^{\mathrm{old}}(\Gamma_1(1925)) \cong$$ $$S_{2}^{\mathrm{new}}(\Gamma_1(11))$$$$^{\oplus 6}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(25))$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(35))$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(55))$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(77))$$$$^{\oplus 3}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(175))$$$$^{\oplus 2}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(275))$$$$^{\oplus 2}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(385))$$$$^{\oplus 2}$$