# Properties

 Label 25.4 Level 25 Weight 4 Dimension 59 Nonzero newspaces 4 Newform subspaces 7 Sturm bound 200 Trace bound 1

## Defining parameters

 Level: $$N$$ = $$25 = 5^{2}$$ Weight: $$k$$ = $$4$$ Nonzero newspaces: $$4$$ Newform subspaces: $$7$$ Sturm bound: $$200$$ Trace bound: $$1$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{4}(\Gamma_1(25))$$.

Total New Old
Modular forms 89 80 9
Cusp forms 61 59 2
Eisenstein series 28 21 7

## Trace form

 $$59 q - 2 q^{2} - 14 q^{3} - 26 q^{4} - 5 q^{5} - 2 q^{6} - 22 q^{7} - 10 q^{8} + 36 q^{9} + O(q^{10})$$ $$59 q - 2 q^{2} - 14 q^{3} - 26 q^{4} - 5 q^{5} - 2 q^{6} - 22 q^{7} - 10 q^{8} + 36 q^{9} - 30 q^{10} - 82 q^{11} - 42 q^{12} + 66 q^{13} + 38 q^{14} - 146 q^{16} - 382 q^{17} - 644 q^{18} - 330 q^{19} + 170 q^{20} + 198 q^{21} + 966 q^{22} + 586 q^{23} + 1420 q^{24} + 685 q^{25} + 108 q^{26} + 730 q^{27} + 614 q^{28} + 170 q^{29} - 290 q^{30} - 162 q^{31} - 1642 q^{32} - 1098 q^{33} - 1452 q^{34} - 840 q^{35} - 1026 q^{36} - 1077 q^{37} - 1700 q^{38} - 2298 q^{39} - 2060 q^{40} - 522 q^{41} - 614 q^{42} - 614 q^{43} + 808 q^{44} + 2195 q^{45} + 1578 q^{46} + 2738 q^{47} + 6276 q^{48} + 2799 q^{49} + 4500 q^{50} + 2688 q^{51} + 4388 q^{52} + 1651 q^{53} + 2960 q^{54} + 910 q^{55} - 110 q^{56} - 970 q^{57} - 2020 q^{58} - 4310 q^{59} - 11470 q^{60} - 2802 q^{61} - 11144 q^{62} - 7954 q^{63} - 6696 q^{64} - 1955 q^{65} - 1114 q^{66} + 458 q^{67} + 3414 q^{68} + 3382 q^{69} + 4190 q^{70} + 1638 q^{71} + 9240 q^{72} + 4626 q^{73} + 9508 q^{74} + 5860 q^{75} + 3620 q^{76} + 5046 q^{77} + 5312 q^{78} + 950 q^{79} + 5830 q^{80} - 2496 q^{81} - 6674 q^{82} - 7354 q^{83} - 13402 q^{84} - 9645 q^{85} - 4942 q^{86} - 8470 q^{87} - 12610 q^{88} - 7335 q^{89} - 8160 q^{90} - 1362 q^{91} - 3742 q^{92} + 4582 q^{93} + 6918 q^{94} + 6810 q^{95} + 4778 q^{96} + 12238 q^{97} + 11034 q^{98} + 13332 q^{99} + O(q^{100})$$

## Decomposition of $$S_{4}^{\mathrm{new}}(\Gamma_1(25))$$

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
25.4.a $$\chi_{25}(1, \cdot)$$ 25.4.a.a 1 1
25.4.a.b 1
25.4.a.c 1
25.4.b $$\chi_{25}(24, \cdot)$$ 25.4.b.a 2 1
25.4.b.b 2
25.4.d $$\chi_{25}(6, \cdot)$$ 25.4.d.a 28 4
25.4.e $$\chi_{25}(4, \cdot)$$ 25.4.e.a 24 4

## Decomposition of $$S_{4}^{\mathrm{old}}(\Gamma_1(25))$$ into lower level spaces

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