# Properties

 Label 2075.2 Level 2075 Weight 2 Dimension 157006 Nonzero newspaces 12 Sturm bound 688800 Trace bound 2

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## Defining parameters

 Level: $$N$$ = $$2075 = 5^{2} \cdot 83$$ Weight: $$k$$ = $$2$$ Nonzero newspaces: $$12$$ Sturm bound: $$688800$$ Trace bound: $$2$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{2}(\Gamma_1(2075))$$.

Total New Old
Modular forms 174496 160326 14170
Cusp forms 169905 157006 12899
Eisenstein series 4591 3320 1271

## Trace form

 $$157006 q - 519 q^{2} - 521 q^{3} - 527 q^{4} - 646 q^{5} - 849 q^{6} - 529 q^{7} - 543 q^{8} - 539 q^{9} + O(q^{10})$$ $$157006 q - 519 q^{2} - 521 q^{3} - 527 q^{4} - 646 q^{5} - 849 q^{6} - 529 q^{7} - 543 q^{8} - 539 q^{9} - 666 q^{10} - 849 q^{11} - 569 q^{12} - 541 q^{13} - 561 q^{14} - 676 q^{15} - 855 q^{16} - 529 q^{17} - 541 q^{18} - 513 q^{19} - 636 q^{20} - 849 q^{21} - 505 q^{22} - 521 q^{23} - 493 q^{24} - 626 q^{25} - 1669 q^{26} - 533 q^{27} - 505 q^{28} - 533 q^{29} - 676 q^{30} - 849 q^{31} - 569 q^{32} - 569 q^{33} - 571 q^{34} - 696 q^{35} - 895 q^{36} - 579 q^{37} - 573 q^{38} - 545 q^{39} - 686 q^{40} - 869 q^{41} - 505 q^{42} - 521 q^{43} - 541 q^{44} - 606 q^{45} - 849 q^{46} - 529 q^{47} - 461 q^{48} - 517 q^{49} - 606 q^{50} - 1649 q^{51} - 489 q^{52} - 531 q^{53} - 493 q^{54} - 676 q^{55} - 881 q^{56} - 513 q^{57} - 553 q^{58} - 533 q^{59} - 636 q^{60} - 869 q^{61} - 485 q^{62} - 541 q^{63} - 547 q^{64} - 666 q^{65} - 938 q^{66} - 610 q^{67} - 689 q^{68} - 688 q^{69} - 716 q^{70} - 930 q^{71} - 973 q^{72} - 704 q^{73} - 603 q^{74} - 676 q^{75} - 1845 q^{76} - 668 q^{77} - 999 q^{78} - 716 q^{79} - 666 q^{80} - 1079 q^{81} - 730 q^{82} - 620 q^{83} - 1586 q^{84} - 586 q^{85} - 1013 q^{86} - 657 q^{87} - 883 q^{88} - 566 q^{89} - 606 q^{90} - 972 q^{91} - 733 q^{92} - 796 q^{93} - 563 q^{94} - 676 q^{95} - 1299 q^{96} - 470 q^{97} - 699 q^{98} - 688 q^{99} + O(q^{100})$$

## Decomposition of $$S_{2}^{\mathrm{new}}(\Gamma_1(2075))$$

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
2075.2.a $$\chi_{2075}(1, \cdot)$$ 2075.2.a.a 1 1
2075.2.a.b 1
2075.2.a.c 1
2075.2.a.d 1
2075.2.a.e 2
2075.2.a.f 6
2075.2.a.g 6
2075.2.a.h 7
2075.2.a.i 8
2075.2.a.j 8
2075.2.a.k 11
2075.2.a.l 19
2075.2.a.m 19
2075.2.a.n 20
2075.2.a.o 20
2075.2.b $$\chi_{2075}(499, \cdot)$$ n/a 124 1
2075.2.e $$\chi_{2075}(82, \cdot)$$ n/a 248 2
2075.2.g $$\chi_{2075}(416, \cdot)$$ n/a 824 4
2075.2.j $$\chi_{2075}(84, \cdot)$$ n/a 816 4
2075.2.l $$\chi_{2075}(248, \cdot)$$ n/a 1664 8
2075.2.m $$\chi_{2075}(26, \cdot)$$ n/a 5200 40
2075.2.p $$\chi_{2075}(49, \cdot)$$ n/a 4960 40
2075.2.r $$\chi_{2075}(18, \cdot)$$ n/a 9920 80
2075.2.s $$\chi_{2075}(11, \cdot)$$ n/a 33280 160
2075.2.t $$\chi_{2075}(4, \cdot)$$ n/a 33280 160
2075.2.w $$\chi_{2075}(2, \cdot)$$ n/a 66560 320

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

## Decomposition of $$S_{2}^{\mathrm{old}}(\Gamma_1(2075))$$ into lower level spaces

$$S_{2}^{\mathrm{old}}(\Gamma_1(2075)) \cong$$ $$S_{2}^{\mathrm{new}}(\Gamma_1(25))$$$$^{\oplus 2}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(83))$$$$^{\oplus 3}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(415))$$$$^{\oplus 2}$$