## Defining parameters

 Level: $$N$$ = $$245 = 5 \cdot 7^{2}$$ Weight: $$k$$ = $$6$$ Nonzero newspaces: $$12$$ Sturm bound: $$28224$$ Trace bound: $$2$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{6}(\Gamma_1(245))$$.

Total New Old
Modular forms 12000 10489 1511
Cusp forms 11520 10199 1321
Eisenstein series 480 290 190

## Trace form

 $$10199 q - 28 q^{2} - 70 q^{3} + 174 q^{4} - 176 q^{5} - 710 q^{6} - 268 q^{7} - 858 q^{8} + 3013 q^{9} + O(q^{10})$$ $$10199 q - 28 q^{2} - 70 q^{3} + 174 q^{4} - 176 q^{5} - 710 q^{6} - 268 q^{7} - 858 q^{8} + 3013 q^{9} + 2655 q^{10} + 1094 q^{11} - 9146 q^{12} - 9084 q^{13} - 3516 q^{14} + 2975 q^{15} + 12454 q^{16} + 8000 q^{17} + 14708 q^{18} - 11414 q^{19} - 9067 q^{20} - 2370 q^{21} + 394 q^{22} + 18654 q^{23} + 37494 q^{24} + 12652 q^{25} + 590 q^{26} - 44818 q^{27} - 46420 q^{28} - 67292 q^{29} - 92747 q^{30} - 24030 q^{31} + 96586 q^{32} + 200158 q^{33} + 268770 q^{34} + 69663 q^{35} + 339782 q^{36} + 116036 q^{37} - 143578 q^{38} - 316744 q^{39} - 451999 q^{40} - 334652 q^{41} - 446754 q^{42} - 232230 q^{43} - 187058 q^{44} + 138583 q^{45} + 564626 q^{46} + 504194 q^{47} + 1068496 q^{48} + 403016 q^{49} + 263258 q^{50} + 326770 q^{51} + 252758 q^{52} + 13136 q^{53} - 638330 q^{54} - 72862 q^{55} - 809688 q^{56} - 500530 q^{57} - 1022350 q^{58} - 674602 q^{59} - 1190735 q^{60} - 393742 q^{61} - 165018 q^{62} + 577860 q^{63} + 457414 q^{64} + 311143 q^{65} + 1333034 q^{66} + 507818 q^{67} + 664678 q^{68} + 524622 q^{69} + 713835 q^{70} + 615358 q^{71} + 1456122 q^{72} + 904920 q^{73} + 739618 q^{74} - 120811 q^{75} - 654134 q^{76} - 195930 q^{77} - 1689902 q^{78} - 1065522 q^{79} - 715408 q^{80} - 175487 q^{81} - 894184 q^{82} - 1353582 q^{83} - 3003156 q^{84} - 109119 q^{85} - 1127212 q^{86} - 1146274 q^{87} - 2060820 q^{88} - 712596 q^{89} - 1418212 q^{90} - 237746 q^{91} - 1458960 q^{92} + 393318 q^{93} + 601788 q^{94} + 389605 q^{95} + 5427332 q^{96} + 2631178 q^{97} + 5712912 q^{98} + 2785820 q^{99} + O(q^{100})$$

## Decomposition of $$S_{6}^{\mathrm{new}}(\Gamma_1(245))$$

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
245.6.a $$\chi_{245}(1, \cdot)$$ 245.6.a.a 1 1
245.6.a.b 1
245.6.a.c 2
245.6.a.d 3
245.6.a.e 4
245.6.a.f 5
245.6.a.g 5
245.6.a.h 6
245.6.a.i 6
245.6.a.j 8
245.6.a.k 8
245.6.a.l 10
245.6.a.m 10
245.6.b $$\chi_{245}(99, \cdot)$$ 245.6.b.a 2 1
245.6.b.b 2
245.6.b.c 12
245.6.b.d 14
245.6.b.e 18
245.6.b.f 18
245.6.b.g 32
245.6.e $$\chi_{245}(116, \cdot)$$ n/a 132 2
245.6.f $$\chi_{245}(48, \cdot)$$ n/a 192 2
245.6.j $$\chi_{245}(79, \cdot)$$ n/a 192 2
245.6.k $$\chi_{245}(36, \cdot)$$ n/a 552 6
245.6.l $$\chi_{245}(68, \cdot)$$ n/a 384 4
245.6.p $$\chi_{245}(29, \cdot)$$ n/a 828 6
245.6.q $$\chi_{245}(11, \cdot)$$ n/a 1128 12
245.6.s $$\chi_{245}(13, \cdot)$$ n/a 1656 12
245.6.t $$\chi_{245}(4, \cdot)$$ n/a 1656 12
245.6.x $$\chi_{245}(3, \cdot)$$ n/a 3312 24

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

## Decomposition of $$S_{6}^{\mathrm{old}}(\Gamma_1(245))$$ into lower level spaces

$$S_{6}^{\mathrm{old}}(\Gamma_1(245)) \cong$$ $$S_{6}^{\mathrm{new}}(\Gamma_1(5))$$$$^{\oplus 3}$$$$\oplus$$$$S_{6}^{\mathrm{new}}(\Gamma_1(7))$$$$^{\oplus 4}$$$$\oplus$$$$S_{6}^{\mathrm{new}}(\Gamma_1(35))$$$$^{\oplus 2}$$$$\oplus$$$$S_{6}^{\mathrm{new}}(\Gamma_1(49))$$$$^{\oplus 2}$$