# Properties

 Label 3025.2 Level 3025 Weight 2 Dimension 326177 Nonzero newspaces 42 Sturm bound 1452000 Trace bound 6

## Defining parameters

 Level: $$N$$ = $$3025 = 5^{2} \cdot 11^{2}$$ Weight: $$k$$ = $$2$$ Nonzero newspaces: $$42$$ Sturm bound: $$1452000$$ Trace bound: $$6$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{2}(\Gamma_1(3025))$$.

Total New Old
Modular forms 367480 331938 35542
Cusp forms 358521 326177 32344
Eisenstein series 8959 5761 3198

## Trace form

 $$326177 q - 592 q^{2} - 591 q^{3} - 588 q^{4} - 725 q^{5} - 941 q^{6} - 577 q^{7} - 560 q^{8} - 562 q^{9} + O(q^{10})$$ $$326177 q - 592 q^{2} - 591 q^{3} - 588 q^{4} - 725 q^{5} - 941 q^{6} - 577 q^{7} - 560 q^{8} - 562 q^{9} - 715 q^{10} - 1045 q^{11} - 1047 q^{12} - 571 q^{13} - 541 q^{14} - 710 q^{15} - 888 q^{16} - 557 q^{17} - 521 q^{18} - 565 q^{19} - 730 q^{20} - 901 q^{21} - 620 q^{22} - 1081 q^{23} - 495 q^{24} - 735 q^{25} - 1761 q^{26} - 525 q^{27} - 489 q^{28} - 535 q^{29} - 710 q^{30} - 911 q^{31} - 467 q^{32} - 610 q^{33} - 1006 q^{34} - 700 q^{35} - 748 q^{36} - 502 q^{37} - 455 q^{38} - 469 q^{39} - 865 q^{40} - 851 q^{41} - 569 q^{42} - 661 q^{43} - 740 q^{44} - 1505 q^{45} - 1141 q^{46} - 757 q^{47} - 1031 q^{48} - 883 q^{49} - 905 q^{50} - 2051 q^{51} - 1077 q^{52} - 716 q^{53} - 1075 q^{54} - 880 q^{55} - 2195 q^{56} - 765 q^{57} - 1045 q^{58} - 725 q^{59} - 1050 q^{60} - 1171 q^{61} - 719 q^{62} - 791 q^{63} - 958 q^{64} - 835 q^{65} - 1085 q^{66} - 1197 q^{67} - 659 q^{68} - 549 q^{69} - 770 q^{70} - 791 q^{71} - 670 q^{72} - 431 q^{73} - 361 q^{74} - 710 q^{75} - 1575 q^{76} - 565 q^{77} - 777 q^{78} - 385 q^{79} - 715 q^{80} - 688 q^{81} - 379 q^{82} - 451 q^{83} - 461 q^{84} - 755 q^{85} - 721 q^{86} - 375 q^{87} - 490 q^{88} - 1020 q^{89} - 1105 q^{90} - 881 q^{91} - 637 q^{92} - 817 q^{93} - 861 q^{94} - 870 q^{95} - 1541 q^{96} - 917 q^{97} - 1144 q^{98} - 910 q^{99} + O(q^{100})$$

## Decomposition of $$S_{2}^{\mathrm{new}}(\Gamma_1(3025))$$

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
3025.2.a $$\chi_{3025}(1, \cdot)$$ 3025.2.a.a 1 1
3025.2.a.b 1
3025.2.a.c 1
3025.2.a.d 1
3025.2.a.e 1
3025.2.a.f 1
3025.2.a.g 1
3025.2.a.h 2
3025.2.a.i 2
3025.2.a.j 2
3025.2.a.k 2
3025.2.a.l 2
3025.2.a.m 2
3025.2.a.n 2
3025.2.a.o 2
3025.2.a.p 3
3025.2.a.q 3
3025.2.a.r 3
3025.2.a.s 3
3025.2.a.t 3
3025.2.a.u 3
3025.2.a.v 4
3025.2.a.w 4
3025.2.a.x 4
3025.2.a.y 4
3025.2.a.z 4
3025.2.a.ba 4
3025.2.a.bb 4
3025.2.a.bc 4
3025.2.a.bd 4
3025.2.a.be 4
3025.2.a.bf 6
3025.2.a.bg 6
3025.2.a.bh 6
3025.2.a.bi 8
3025.2.a.bj 8
3025.2.a.bk 8
3025.2.a.bl 8
3025.2.a.bm 8
3025.2.a.bn 8
3025.2.a.bo 12
3025.2.b $$\chi_{3025}(1574, \cdot)$$ n/a 154 1
3025.2.e $$\chi_{3025}(1693, \cdot)$$ n/a 308 2
3025.2.g $$\chi_{3025}(1116, \cdot)$$ n/a 1048 4
3025.2.h $$\chi_{3025}(251, \cdot)$$ n/a 636 4
3025.2.i $$\chi_{3025}(606, \cdot)$$ n/a 1052 4
3025.2.j $$\chi_{3025}(81, \cdot)$$ n/a 1048 4
3025.2.k $$\chi_{3025}(1291, \cdot)$$ n/a 1048 4
3025.2.l $$\chi_{3025}(366, \cdot)$$ n/a 1048 4
3025.2.n $$\chi_{3025}(1219, \cdot)$$ n/a 1048 4
3025.2.t $$\chi_{3025}(269, \cdot)$$ n/a 1048 4
3025.2.y $$\chi_{3025}(364, \cdot)$$ n/a 1056 4
3025.2.z $$\chi_{3025}(124, \cdot)$$ n/a 616 4
3025.2.ba $$\chi_{3025}(614, \cdot)$$ n/a 1048 4
3025.2.bb $$\chi_{3025}(9, \cdot)$$ n/a 1048 4
3025.2.be $$\chi_{3025}(276, \cdot)$$ n/a 2060 10
3025.2.bg $$\chi_{3025}(233, \cdot)$$ n/a 2096 8
3025.2.bh $$\chi_{3025}(112, \cdot)$$ n/a 2096 8
3025.2.bm $$\chi_{3025}(602, \cdot)$$ n/a 2096 8
3025.2.bn $$\chi_{3025}(118, \cdot)$$ n/a 1232 8
3025.2.bo $$\chi_{3025}(403, \cdot)$$ n/a 2096 8
3025.2.bp $$\chi_{3025}(362, \cdot)$$ n/a 2096 8
3025.2.bs $$\chi_{3025}(199, \cdot)$$ n/a 1960 10
3025.2.bv $$\chi_{3025}(32, \cdot)$$ n/a 3920 20
3025.2.bw $$\chi_{3025}(31, \cdot)$$ n/a 13120 40
3025.2.bx $$\chi_{3025}(141, \cdot)$$ n/a 13120 40
3025.2.by $$\chi_{3025}(56, \cdot)$$ n/a 13120 40
3025.2.bz $$\chi_{3025}(26, \cdot)$$ n/a 8240 40
3025.2.ca $$\chi_{3025}(16, \cdot)$$ n/a 13120 40
3025.2.cb $$\chi_{3025}(36, \cdot)$$ n/a 13120 40
3025.2.cd $$\chi_{3025}(14, \cdot)$$ n/a 13120 40
3025.2.ci $$\chi_{3025}(169, \cdot)$$ n/a 13120 40
3025.2.cj $$\chi_{3025}(4, \cdot)$$ n/a 13120 40
3025.2.ck $$\chi_{3025}(49, \cdot)$$ n/a 7840 40
3025.2.cl $$\chi_{3025}(34, \cdot)$$ n/a 13120 40
3025.2.ct $$\chi_{3025}(104, \cdot)$$ n/a 13120 40
3025.2.cv $$\chi_{3025}(17, \cdot)$$ n/a 26240 80
3025.2.cw $$\chi_{3025}(87, \cdot)$$ n/a 26240 80
3025.2.cx $$\chi_{3025}(2, \cdot)$$ n/a 26240 80
3025.2.cy $$\chi_{3025}(7, \cdot)$$ n/a 15680 80
3025.2.dd $$\chi_{3025}(13, \cdot)$$ n/a 26240 80
3025.2.de $$\chi_{3025}(28, \cdot)$$ n/a 26240 80

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

## Decomposition of $$S_{2}^{\mathrm{old}}(\Gamma_1(3025))$$ into lower level spaces

$$S_{2}^{\mathrm{old}}(\Gamma_1(3025)) \cong$$ $$S_{2}^{\mathrm{new}}(\Gamma_1(11))$$$$^{\oplus 6}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(25))$$$$^{\oplus 3}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(55))$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(121))$$$$^{\oplus 3}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(275))$$$$^{\oplus 2}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(605))$$$$^{\oplus 2}$$