# Properties

 Label 650.6 Level 650 Weight 6 Dimension 19125 Nonzero newspaces 24 Sturm bound 151200 Trace bound 5

## Defining parameters

 Level: $$N$$ = $$650 = 2 \cdot 5^{2} \cdot 13$$ Weight: $$k$$ = $$6$$ Nonzero newspaces: $$24$$ Sturm bound: $$151200$$ Trace bound: $$5$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{6}(\Gamma_1(650))$$.

Total New Old
Modular forms 63672 19125 44547
Cusp forms 62328 19125 43203
Eisenstein series 1344 0 1344

## Trace form

 $$19125 q - 16 q^{2} + 16 q^{3} + 64 q^{4} + 170 q^{5} - 320 q^{6} - 652 q^{7} - 448 q^{8} + 1316 q^{9} + O(q^{10})$$ $$19125 q - 16 q^{2} + 16 q^{3} + 64 q^{4} + 170 q^{5} - 320 q^{6} - 652 q^{7} - 448 q^{8} + 1316 q^{9} - 360 q^{10} - 1892 q^{11} + 832 q^{12} + 3372 q^{13} + 6800 q^{14} + 1640 q^{15} + 4096 q^{16} - 4937 q^{17} - 4228 q^{18} + 7564 q^{19} - 1280 q^{20} + 4372 q^{21} - 5632 q^{22} - 21076 q^{23} - 13824 q^{24} - 50670 q^{25} - 1760 q^{26} - 16484 q^{27} + 1728 q^{28} + 72935 q^{29} + 60000 q^{30} - 1512 q^{31} + 6144 q^{32} + 71652 q^{33} + 22152 q^{34} - 121720 q^{35} + 50880 q^{36} - 75203 q^{37} - 17456 q^{38} + 28188 q^{39} - 640 q^{40} + 103823 q^{41} + 45712 q^{42} + 114572 q^{43} - 45952 q^{44} - 3670 q^{45} - 23200 q^{46} - 48016 q^{47} + 4096 q^{48} - 320606 q^{49} - 160792 q^{50} - 755056 q^{51} + 25328 q^{52} + 102306 q^{53} + 698928 q^{54} + 676536 q^{55} + 234240 q^{56} + 1583416 q^{57} + 452436 q^{58} + 125096 q^{59} - 318976 q^{60} - 752485 q^{61} - 603824 q^{62} - 1880204 q^{63} - 69632 q^{64} - 436087 q^{65} - 981920 q^{66} - 471492 q^{67} + 195696 q^{68} + 384600 q^{69} + 101696 q^{70} + 244712 q^{71} + 514304 q^{72} + 819648 q^{73} + 299748 q^{74} - 114760 q^{75} + 343744 q^{76} - 104600 q^{77} + 144256 q^{78} - 1599872 q^{79} - 82432 q^{80} - 3315400 q^{81} - 171020 q^{82} + 500640 q^{83} + 401088 q^{84} + 1669010 q^{85} + 805056 q^{86} + 3245824 q^{87} + 211968 q^{88} + 961774 q^{89} - 488040 q^{90} + 439324 q^{91} - 582400 q^{92} - 849488 q^{93} - 358288 q^{94} - 759080 q^{95} - 81920 q^{96} - 847884 q^{97} + 351600 q^{98} - 2829532 q^{99} + O(q^{100})$$

## Decomposition of $$S_{6}^{\mathrm{new}}(\Gamma_1(650))$$

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 available newforms together with their dimension.

Label $$\chi$$ Newforms Dimension $$\chi$$ degree
650.6.a $$\chi_{650}(1, \cdot)$$ 650.6.a.a 1 1
650.6.a.b 2
650.6.a.c 2
650.6.a.d 2
650.6.a.e 2
650.6.a.f 2
650.6.a.g 2
650.6.a.h 2
650.6.a.i 3
650.6.a.j 3
650.6.a.k 4
650.6.a.l 4
650.6.a.m 4
650.6.a.n 5
650.6.a.o 5
650.6.a.p 5
650.6.a.q 5
650.6.a.r 6
650.6.a.s 6
650.6.a.t 6
650.6.a.u 6
650.6.a.v 9
650.6.a.w 9
650.6.b $$\chi_{650}(599, \cdot)$$ 650.6.b.a 2 1
650.6.b.b 4
650.6.b.c 4
650.6.b.d 4
650.6.b.e 4
650.6.b.f 4
650.6.b.g 4
650.6.b.h 4
650.6.b.i 6
650.6.b.j 6
650.6.b.k 8
650.6.b.l 8
650.6.b.m 10
650.6.b.n 10
650.6.b.o 12
650.6.c $$\chi_{650}(649, \cdot)$$ n/a 104 1
650.6.d $$\chi_{650}(51, \cdot)$$ n/a 110 1
650.6.e $$\chi_{650}(451, \cdot)$$ n/a 222 2
650.6.g $$\chi_{650}(57, \cdot)$$ n/a 210 2
650.6.j $$\chi_{650}(307, \cdot)$$ n/a 210 2
650.6.l $$\chi_{650}(131, \cdot)$$ n/a 600 4
650.6.m $$\chi_{650}(101, \cdot)$$ n/a 224 2
650.6.n $$\chi_{650}(49, \cdot)$$ n/a 208 2
650.6.o $$\chi_{650}(399, \cdot)$$ n/a 212 2
650.6.p $$\chi_{650}(181, \cdot)$$ n/a 696 4
650.6.q $$\chi_{650}(79, \cdot)$$ n/a 600 4
650.6.r $$\chi_{650}(129, \cdot)$$ n/a 704 4
650.6.t $$\chi_{650}(7, \cdot)$$ n/a 420 4
650.6.w $$\chi_{650}(193, \cdot)$$ n/a 420 4
650.6.y $$\chi_{650}(61, \cdot)$$ n/a 1408 8
650.6.ba $$\chi_{650}(73, \cdot)$$ n/a 1400 8
650.6.bd $$\chi_{650}(47, \cdot)$$ n/a 1400 8
650.6.bf $$\chi_{650}(69, \cdot)$$ n/a 1408 8
650.6.bg $$\chi_{650}(9, \cdot)$$ n/a 1392 8
650.6.bh $$\chi_{650}(121, \cdot)$$ n/a 1392 8
650.6.bj $$\chi_{650}(37, \cdot)$$ n/a 2800 16
650.6.bm $$\chi_{650}(33, \cdot)$$ n/a 2800 16

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

## Decomposition of $$S_{6}^{\mathrm{old}}(\Gamma_1(650))$$ into lower level spaces

$$S_{6}^{\mathrm{old}}(\Gamma_1(650)) \cong$$ $$S_{6}^{\mathrm{new}}(\Gamma_1(1))$$$$^{\oplus 12}$$$$\oplus$$$$S_{6}^{\mathrm{new}}(\Gamma_1(2))$$$$^{\oplus 6}$$$$\oplus$$$$S_{6}^{\mathrm{new}}(\Gamma_1(5))$$$$^{\oplus 8}$$$$\oplus$$$$S_{6}^{\mathrm{new}}(\Gamma_1(10))$$$$^{\oplus 4}$$$$\oplus$$$$S_{6}^{\mathrm{new}}(\Gamma_1(13))$$$$^{\oplus 6}$$$$\oplus$$$$S_{6}^{\mathrm{new}}(\Gamma_1(25))$$$$^{\oplus 4}$$$$\oplus$$$$S_{6}^{\mathrm{new}}(\Gamma_1(26))$$$$^{\oplus 3}$$$$\oplus$$$$S_{6}^{\mathrm{new}}(\Gamma_1(50))$$$$^{\oplus 2}$$$$\oplus$$$$S_{6}^{\mathrm{new}}(\Gamma_1(65))$$$$^{\oplus 4}$$$$\oplus$$$$S_{6}^{\mathrm{new}}(\Gamma_1(130))$$$$^{\oplus 2}$$$$\oplus$$$$S_{6}^{\mathrm{new}}(\Gamma_1(325))$$$$^{\oplus 2}$$$$\oplus$$$$S_{6}^{\mathrm{new}}(\Gamma_1(650))$$$$^{\oplus 1}$$