# Properties

 Label 2601.2 Level 2601 Weight 2 Dimension 194652 Nonzero newspaces 20 Sturm bound 998784 Trace bound 4

## Defining parameters

 Level: $$N$$ = $$2601 = 3^{2} \cdot 17^{2}$$ Weight: $$k$$ = $$2$$ Nonzero newspaces: $$20$$ Sturm bound: $$998784$$ Trace bound: $$4$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{2}(\Gamma_1(2601))$$.

Total New Old
Modular forms 252896 197969 54927
Cusp forms 246497 194652 51845
Eisenstein series 6399 3317 3082

## Trace form

 $$194652q - 360q^{2} - 480q^{3} - 360q^{4} - 360q^{5} - 480q^{6} - 360q^{7} - 360q^{8} - 480q^{9} + O(q^{10})$$ $$194652q - 360q^{2} - 480q^{3} - 360q^{4} - 360q^{5} - 480q^{6} - 360q^{7} - 360q^{8} - 480q^{9} - 1072q^{10} - 344q^{11} - 480q^{12} - 344q^{13} - 328q^{14} - 480q^{15} - 288q^{16} - 376q^{17} - 928q^{18} - 1064q^{19} - 304q^{20} - 480q^{21} - 328q^{22} - 344q^{23} - 480q^{24} - 304q^{25} - 288q^{26} - 480q^{27} - 984q^{28} - 320q^{29} - 480q^{30} - 296q^{31} - 376q^{32} - 480q^{33} - 320q^{34} - 632q^{35} - 480q^{36} - 1016q^{37} - 328q^{38} - 544q^{39} - 424q^{40} - 464q^{41} - 672q^{42} - 408q^{43} - 680q^{44} - 608q^{45} - 1240q^{46} - 600q^{47} - 800q^{48} - 552q^{49} - 744q^{50} - 576q^{51} - 1080q^{52} - 528q^{53} - 704q^{54} - 1208q^{55} - 760q^{56} - 640q^{57} - 440q^{58} - 488q^{59} - 736q^{60} - 360q^{61} - 536q^{62} - 576q^{63} - 1112q^{64} - 336q^{65} - 576q^{66} - 280q^{67} - 284q^{68} - 928q^{69} - 88q^{70} - 264q^{71} - 608q^{72} - 880q^{73} - 192q^{74} - 480q^{75} - 120q^{76} - 200q^{77} - 480q^{78} - 232q^{79} - 328q^{80} - 480q^{81} - 864q^{82} - 296q^{83} - 640q^{84} - 420q^{85} - 1112q^{86} - 672q^{87} - 552q^{88} - 600q^{89} - 960q^{90} - 1368q^{91} - 872q^{92} - 736q^{93} - 808q^{94} - 776q^{95} - 1088q^{96} - 488q^{97} - 1104q^{98} - 768q^{99} + O(q^{100})$$

## Decomposition of $$S_{2}^{\mathrm{new}}(\Gamma_1(2601))$$

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
2601.2.a $$\chi_{2601}(1, \cdot)$$ 2601.2.a.a 1 1
2601.2.a.b 1
2601.2.a.c 1
2601.2.a.d 1
2601.2.a.e 1
2601.2.a.f 1
2601.2.a.g 1
2601.2.a.h 1
2601.2.a.i 1
2601.2.a.j 1
2601.2.a.k 1
2601.2.a.l 1
2601.2.a.m 2
2601.2.a.n 2
2601.2.a.o 2
2601.2.a.p 2
2601.2.a.q 2
2601.2.a.r 2
2601.2.a.s 2
2601.2.a.t 2
2601.2.a.u 3
2601.2.a.v 3
2601.2.a.w 3
2601.2.a.x 3
2601.2.a.y 3
2601.2.a.z 3
2601.2.a.ba 4
2601.2.a.bb 4
2601.2.a.bc 4
2601.2.a.bd 4
2601.2.a.be 4
2601.2.a.bf 4
2601.2.a.bg 4
2601.2.a.bh 6
2601.2.a.bi 6
2601.2.a.bj 6
2601.2.a.bk 6
2601.2.a.bl 8
2601.2.d $$\chi_{2601}(577, \cdot)$$ n/a 106 1
2601.2.e $$\chi_{2601}(868, \cdot)$$ n/a 512 2
2601.2.f $$\chi_{2601}(829, \cdot)$$ n/a 212 2
2601.2.h $$\chi_{2601}(1444, \cdot)$$ n/a 512 2
2601.2.l $$\chi_{2601}(712, \cdot)$$ n/a 420 4
2601.2.n $$\chi_{2601}(616, \cdot)$$ n/a 1024 4
2601.2.o $$\chi_{2601}(224, \cdot)$$ n/a 720 8
2601.2.q $$\chi_{2601}(154, \cdot)$$ n/a 2016 16
2601.2.s $$\chi_{2601}(688, \cdot)$$ n/a 2048 8
2601.2.t $$\chi_{2601}(118, \cdot)$$ n/a 2016 16
2601.2.w $$\chi_{2601}(65, \cdot)$$ n/a 4096 16
2601.2.y $$\chi_{2601}(52, \cdot)$$ n/a 9728 32
2601.2.ba $$\chi_{2601}(55, \cdot)$$ n/a 4032 32
2601.2.bd $$\chi_{2601}(16, \cdot)$$ n/a 9728 32
2601.2.be $$\chi_{2601}(19, \cdot)$$ n/a 8128 64
2601.2.bg $$\chi_{2601}(4, \cdot)$$ n/a 19456 64
2601.2.bj $$\chi_{2601}(44, \cdot)$$ n/a 13056 128
2601.2.bk $$\chi_{2601}(25, \cdot)$$ n/a 38912 128
2601.2.bn $$\chi_{2601}(5, \cdot)$$ n/a 77824 256

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

## Decomposition of $$S_{2}^{\mathrm{old}}(\Gamma_1(2601))$$ into lower level spaces

$$S_{2}^{\mathrm{old}}(\Gamma_1(2601)) \cong$$ $$S_{2}^{\mathrm{new}}(\Gamma_1(17))$$$$^{\oplus 6}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(51))$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(153))$$$$^{\oplus 2}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(289))$$$$^{\oplus 3}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(867))$$$$^{\oplus 2}$$