## Defining parameters

 Level: $$N$$ = $$425 = 5^{2} \cdot 17$$ Weight: $$k$$ = $$4$$ Nonzero newspaces: $$20$$ Sturm bound: $$57600$$ Trace bound: $$8$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{4}(\Gamma_1(425))$$.

Total New Old
Modular forms 22048 20076 1972
Cusp forms 21152 19462 1690
Eisenstein series 896 614 282

## Trace form

 $$19462 q - 100 q^{2} - 76 q^{3} - 52 q^{4} - 118 q^{5} - 164 q^{6} - 60 q^{7} - 84 q^{8} - 176 q^{9} + O(q^{10})$$ $$19462 q - 100 q^{2} - 76 q^{3} - 52 q^{4} - 118 q^{5} - 164 q^{6} - 60 q^{7} - 84 q^{8} - 176 q^{9} - 68 q^{10} - 116 q^{11} - 116 q^{12} - 204 q^{13} - 20 q^{14} - 128 q^{15} + 564 q^{16} + 406 q^{17} + 1528 q^{18} + 636 q^{19} - 468 q^{20} - 660 q^{21} - 2260 q^{22} - 1484 q^{23} - 4816 q^{24} - 1498 q^{25} - 1576 q^{26} - 1780 q^{27} - 1188 q^{28} - 184 q^{29} + 452 q^{30} + 1020 q^{31} + 4356 q^{32} + 3140 q^{33} + 3460 q^{34} + 1424 q^{35} + 3548 q^{36} + 2722 q^{37} + 2968 q^{38} + 3276 q^{39} + 3992 q^{40} - 544 q^{41} - 1804 q^{42} - 340 q^{43} - 3672 q^{44} - 4518 q^{45} - 4332 q^{46} - 4060 q^{47} - 9352 q^{48} - 4166 q^{49} - 9128 q^{50} - 1416 q^{51} - 5912 q^{52} - 3714 q^{53} - 8712 q^{54} - 1948 q^{55} - 948 q^{56} - 252 q^{57} + 2456 q^{58} + 7652 q^{59} + 22812 q^{60} + 5676 q^{61} + 20320 q^{62} + 17772 q^{63} + 15288 q^{64} + 3782 q^{65} + 7236 q^{66} + 1116 q^{67} + 18170 q^{68} + 16740 q^{69} + 7620 q^{70} + 9292 q^{71} + 16032 q^{72} + 6304 q^{73} - 11368 q^{74} - 11080 q^{75} - 13224 q^{76} - 17572 q^{77} - 34016 q^{78} - 16180 q^{79} - 32268 q^{80} - 25808 q^{81} - 29604 q^{82} - 6636 q^{83} - 46092 q^{84} - 6611 q^{85} - 19940 q^{86} - 14604 q^{87} - 28452 q^{88} + 1174 q^{89} + 1504 q^{90} - 12132 q^{91} - 7068 q^{92} - 10100 q^{93} - 6932 q^{94} - 10420 q^{95} + 20844 q^{96} - 5860 q^{97} + 14628 q^{98} + 10944 q^{99} + O(q^{100})$$

## Decomposition of $$S_{4}^{\mathrm{new}}(\Gamma_1(425))$$

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
425.4.a $$\chi_{425}(1, \cdot)$$ 425.4.a.a 1 1
425.4.a.b 1
425.4.a.c 1
425.4.a.d 1
425.4.a.e 2
425.4.a.f 3
425.4.a.g 3
425.4.a.h 3
425.4.a.i 5
425.4.a.j 6
425.4.a.k 6
425.4.a.l 10
425.4.a.m 10
425.4.a.n 12
425.4.a.o 12
425.4.b $$\chi_{425}(324, \cdot)$$ 425.4.b.a 2 1
425.4.b.b 2
425.4.b.c 2
425.4.b.d 2
425.4.b.e 4
425.4.b.f 6
425.4.b.g 6
425.4.b.h 6
425.4.b.i 10
425.4.b.j 12
425.4.b.k 20
425.4.c $$\chi_{425}(424, \cdot)$$ 425.4.c.a 2 1
425.4.c.b 2
425.4.c.c 8
425.4.c.d 8
425.4.c.e 16
425.4.c.f 16
425.4.c.g 28
425.4.d $$\chi_{425}(101, \cdot)$$ 425.4.d.a 2 1
425.4.d.b 4
425.4.d.c 4
425.4.d.d 4
425.4.d.e 14
425.4.d.f 14
425.4.d.g 16
425.4.d.h 24
425.4.e $$\chi_{425}(251, \cdot)$$ n/a 164 2
425.4.j $$\chi_{425}(149, \cdot)$$ n/a 160 2
425.4.k $$\chi_{425}(86, \cdot)$$ n/a 480 4
425.4.m $$\chi_{425}(26, \cdot)$$ n/a 332 4
425.4.n $$\chi_{425}(49, \cdot)$$ n/a 312 4
425.4.p $$\chi_{425}(16, \cdot)$$ n/a 536 4
425.4.q $$\chi_{425}(84, \cdot)$$ n/a 528 4
425.4.r $$\chi_{425}(69, \cdot)$$ n/a 480 4
425.4.s $$\chi_{425}(7, \cdot)$$ n/a 632 8
425.4.v $$\chi_{425}(82, \cdot)$$ n/a 632 8
425.4.w $$\chi_{425}(4, \cdot)$$ n/a 1056 8
425.4.bb $$\chi_{425}(21, \cdot)$$ n/a 1072 8
425.4.bd $$\chi_{425}(9, \cdot)$$ n/a 2144 16
425.4.be $$\chi_{425}(36, \cdot)$$ n/a 2112 16
425.4.bg $$\chi_{425}(12, \cdot)$$ n/a 4256 32
425.4.bj $$\chi_{425}(3, \cdot)$$ n/a 4256 32

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

## Decomposition of $$S_{4}^{\mathrm{old}}(\Gamma_1(425))$$ into lower level spaces

$$S_{4}^{\mathrm{old}}(\Gamma_1(425)) \cong$$ $$S_{4}^{\mathrm{new}}(\Gamma_1(5))$$$$^{\oplus 4}$$$$\oplus$$$$S_{4}^{\mathrm{new}}(\Gamma_1(17))$$$$^{\oplus 3}$$$$\oplus$$$$S_{4}^{\mathrm{new}}(\Gamma_1(25))$$$$^{\oplus 2}$$$$\oplus$$$$S_{4}^{\mathrm{new}}(\Gamma_1(85))$$$$^{\oplus 2}$$