# Properties

 Label 1075.6 Level 1075 Weight 6 Dimension 211834 Nonzero newspaces 24 Sturm bound 554400 Trace bound 4

## Defining parameters

 Level: $$N$$ = $$1075 = 5^{2} \cdot 43$$ Weight: $$k$$ = $$6$$ Nonzero newspaces: $$24$$ Sturm bound: $$554400$$ Trace bound: $$4$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{6}(\Gamma_1(1075))$$.

Total New Old
Modular forms 232176 213514 18662
Cusp forms 229824 211834 17990
Eisenstein series 2352 1680 672

## Trace form

 $$211834 q - 245 q^{2} - 269 q^{3} - 461 q^{4} - 446 q^{5} + 619 q^{6} + 515 q^{7} - 733 q^{8} - 2385 q^{9} + O(q^{10})$$ $$211834 q - 245 q^{2} - 269 q^{3} - 461 q^{4} - 446 q^{5} + 619 q^{6} + 515 q^{7} - 733 q^{8} - 2385 q^{9} - 1096 q^{10} + 1019 q^{11} + 195 q^{12} + 891 q^{13} + 4451 q^{14} + 2124 q^{15} + 299 q^{16} - 3145 q^{17} - 18269 q^{18} - 15333 q^{19} - 20836 q^{20} - 14781 q^{21} + 17443 q^{22} + 30091 q^{23} + 91927 q^{24} + 37694 q^{25} + 23019 q^{26} + 12127 q^{27} - 58237 q^{28} - 97693 q^{29} - 107996 q^{30} - 34424 q^{31} - 111133 q^{32} + 2853 q^{33} + 151119 q^{34} + 80424 q^{35} + 263451 q^{36} + 94487 q^{37} + 156103 q^{38} - 65058 q^{39} - 179816 q^{40} - 156120 q^{41} - 556394 q^{42} - 243416 q^{43} - 231218 q^{44} + 35234 q^{45} - 4957 q^{46} + 98786 q^{47} + 817863 q^{48} + 519678 q^{49} + 504564 q^{50} + 292521 q^{51} + 541287 q^{52} + 217159 q^{53} - 42925 q^{54} - 182596 q^{55} - 698429 q^{56} - 700846 q^{57} - 611193 q^{58} - 329513 q^{59} - 195316 q^{60} + 61619 q^{61} - 187217 q^{62} - 173209 q^{63} - 272321 q^{64} - 272666 q^{65} - 111541 q^{66} + 6915 q^{67} - 154077 q^{68} - 357587 q^{69} + 234964 q^{70} + 480441 q^{71} + 1907037 q^{72} + 483313 q^{73} + 1346626 q^{74} + 621244 q^{75} + 1600036 q^{76} + 1114677 q^{77} + 1328468 q^{78} + 440527 q^{79} - 4316 q^{80} - 647673 q^{81} - 295307 q^{82} - 675925 q^{83} - 4170751 q^{84} - 1362666 q^{85} - 2193563 q^{86} - 3602116 q^{87} - 4032917 q^{88} - 1472463 q^{89} - 1509156 q^{90} - 115697 q^{91} + 1614305 q^{92} + 1638823 q^{93} + 2484651 q^{94} + 847644 q^{95} + 3761042 q^{96} + 3318309 q^{97} + 4461510 q^{98} + 3647208 q^{99} + O(q^{100})$$

## Decomposition of $$S_{6}^{\mathrm{new}}(\Gamma_1(1075))$$

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
1075.6.a $$\chi_{1075}(1, \cdot)$$ 1075.6.a.a 8 1
1075.6.a.b 10
1075.6.a.c 13
1075.6.a.d 15
1075.6.a.e 20
1075.6.a.f 22
1075.6.a.g 33
1075.6.a.h 33
1075.6.a.i 37
1075.6.a.j 37
1075.6.a.k 52
1075.6.a.l 52
1075.6.b $$\chi_{1075}(474, \cdot)$$ n/a 316 1
1075.6.e $$\chi_{1075}(251, \cdot)$$ n/a 690 2
1075.6.g $$\chi_{1075}(257, \cdot)$$ n/a 656 2
1075.6.h $$\chi_{1075}(216, \cdot)$$ n/a 2104 4
1075.6.j $$\chi_{1075}(49, \cdot)$$ n/a 656 2
1075.6.l $$\chi_{1075}(176, \cdot)$$ n/a 2076 6
1075.6.o $$\chi_{1075}(44, \cdot)$$ n/a 2096 4
1075.6.p $$\chi_{1075}(7, \cdot)$$ n/a 1312 4
1075.6.t $$\chi_{1075}(274, \cdot)$$ n/a 1968 6
1075.6.u $$\chi_{1075}(6, \cdot)$$ n/a 4384 8
1075.6.v $$\chi_{1075}(42, \cdot)$$ n/a 4384 8
1075.6.x $$\chi_{1075}(101, \cdot)$$ n/a 4140 12
1075.6.y $$\chi_{1075}(32, \cdot)$$ n/a 3936 12
1075.6.bb $$\chi_{1075}(79, \cdot)$$ n/a 4384 8
1075.6.bd $$\chi_{1075}(11, \cdot)$$ n/a 13152 24
1075.6.bf $$\chi_{1075}(24, \cdot)$$ n/a 3936 12
1075.6.bi $$\chi_{1075}(37, \cdot)$$ n/a 8768 16
1075.6.bj $$\chi_{1075}(4, \cdot)$$ n/a 13152 24
1075.6.bn $$\chi_{1075}(18, \cdot)$$ n/a 7872 24
1075.6.bo $$\chi_{1075}(31, \cdot)$$ n/a 26304 48
1075.6.bq $$\chi_{1075}(2, \cdot)$$ n/a 26304 48
1075.6.bs $$\chi_{1075}(9, \cdot)$$ n/a 26304 48
1075.6.bu $$\chi_{1075}(3, \cdot)$$ n/a 52608 96

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

## Decomposition of $$S_{6}^{\mathrm{old}}(\Gamma_1(1075))$$ into lower level spaces

$$S_{6}^{\mathrm{old}}(\Gamma_1(1075)) \cong$$ $$S_{6}^{\mathrm{new}}(\Gamma_1(5))$$$$^{\oplus 4}$$$$\oplus$$$$S_{6}^{\mathrm{new}}(\Gamma_1(25))$$$$^{\oplus 2}$$$$\oplus$$$$S_{6}^{\mathrm{new}}(\Gamma_1(43))$$$$^{\oplus 3}$$$$\oplus$$$$S_{6}^{\mathrm{new}}(\Gamma_1(215))$$$$^{\oplus 2}$$