# Properties

 Label 25.3 Level 25 Weight 3 Dimension 36 Nonzero newspaces 2 Newform subspaces 2 Sturm bound 150 Trace bound 1

## Defining parameters

 Level: $$N$$ = $$25 = 5^{2}$$ Weight: $$k$$ = $$3$$ Nonzero newspaces: $$2$$ Newform subspaces: $$2$$ Sturm bound: $$150$$ Trace bound: $$1$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{3}(\Gamma_1(25))$$.

Total New Old
Modular forms 64 56 8
Cusp forms 36 36 0
Eisenstein series 28 20 8

## Trace form

 $$36q - 10q^{2} - 10q^{3} - 10q^{4} - 10q^{5} - 18q^{6} - 10q^{7} - 10q^{8} - 10q^{9} + O(q^{10})$$ $$36q - 10q^{2} - 10q^{3} - 10q^{4} - 10q^{5} - 18q^{6} - 10q^{7} - 10q^{8} - 10q^{9} - 10q^{10} - 18q^{11} - 10q^{12} - 10q^{13} - 10q^{14} - 10q^{15} + 46q^{16} + 60q^{17} + 140q^{18} + 90q^{19} + 130q^{20} + 42q^{21} + 70q^{22} + 10q^{23} - 40q^{25} - 68q^{26} - 100q^{27} - 250q^{28} - 110q^{29} - 250q^{30} - 158q^{31} - 290q^{32} - 190q^{33} - 260q^{34} - 120q^{35} - 34q^{36} + 50q^{37} + 320q^{38} + 390q^{39} + 440q^{40} + 142q^{41} + 690q^{42} + 230q^{43} + 340q^{44} + 310q^{45} + 162q^{46} + 70q^{47} + 160q^{48} - 100q^{50} - 148q^{51} - 320q^{52} - 190q^{53} - 660q^{54} - 250q^{55} - 310q^{56} - 650q^{57} - 640q^{58} - 260q^{59} - 550q^{60} + 2q^{61} + 60q^{62} - 20q^{63} + 340q^{64} + 360q^{65} + 174q^{66} + 270q^{67} + 710q^{68} + 340q^{69} + 310q^{70} + 102q^{71} + 360q^{72} + 30q^{73} - 90q^{75} - 60q^{76} - 250q^{77} - 500q^{78} - 210q^{79} - 850q^{80} + 26q^{81} + 30q^{82} - 10q^{84} + 600q^{85} + 42q^{86} + 300q^{87} + 190q^{88} - 10q^{89} + 380q^{90} + 282q^{91} - 30q^{92} + 520q^{93} + 790q^{94} + 310q^{95} + 282q^{96} + 270q^{97} + 170q^{98} + O(q^{100})$$

## Decomposition of $$S_{3}^{\mathrm{new}}(\Gamma_1(25))$$

We only show spaces with odd 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
25.3.c $$\chi_{25}(7, \cdot)$$ 25.3.c.a 4 2
25.3.f $$\chi_{25}(2, \cdot)$$ 25.3.f.a 32 8

## Hecke characteristic polynomials

$p$ $F_p(T)$
$2$ ($$1 - 7 T^{4} + 256 T^{8}$$)
$3$ ($$1 + 63 T^{4} + 6561 T^{8}$$)
$5$ 1
$7$ ($$1 - 2302 T^{4} + 5764801 T^{8}$$)
$11$ ($$( 1 + 3 T + 121 T^{2} )^{4}$$)
$13$ ($$1 - 4222 T^{4} + 815730721 T^{8}$$)
$17$ ($$1 - 120817 T^{4} + 6975757441 T^{8}$$)
$19$ ($$( 1 - 697 T^{2} + 130321 T^{4} )^{2}$$)
$23$ ($$1 - 338782 T^{4} + 78310985281 T^{8}$$)
$29$ ($$( 1 - 782 T^{2} + 707281 T^{4} )^{2}$$)
$31$ ($$( 1 + 38 T + 961 T^{2} )^{4}$$)
$37$ ($$1 + 132578 T^{4} + 3512479453921 T^{8}$$)
$41$ ($$( 1 - 57 T + 1681 T^{2} )^{4}$$)
$43$ ($$1 + 6484898 T^{4} + 11688200277601 T^{8}$$)
$47$ ($$1 + 8816738 T^{4} + 23811286661761 T^{8}$$)
$53$ ($$1 - 2892862 T^{4} + 62259690411361 T^{8}$$)
$59$ ($$( 1 + 1138 T^{2} + 12117361 T^{4} )^{2}$$)
$61$ ($$( 1 + 28 T + 3721 T^{2} )^{4}$$)
$67$ ($$1 - 20810017 T^{4} + 406067677556641 T^{8}$$)
$71$ ($$( 1 - 42 T + 5041 T^{2} )^{4}$$)
$73$ ($$1 + 49190543 T^{4} + 806460091894081 T^{8}$$)
$79$ ($$( 1 - 6082 T^{2} + 38950081 T^{4} )^{2}$$)
$83$ ($$1 + 27517583 T^{4} + 2252292232139041 T^{8}$$)
$89$ ($$( 1 - 15617 T^{2} + 62742241 T^{4} )^{2}$$)
$97$ ($$1 - 7798462 T^{4} + 7837433594376961 T^{8}$$)