# Properties

 Label 25.3.c Level 25 Weight 3 Character orbit c Rep. character $$\chi_{25}(7,\cdot)$$ Character field $$\Q(\zeta_{4})$$ Dimension 4 Newform subspaces 1 Sturm bound 7 Trace bound 0

# Related objects

## Defining parameters

 Level: $$N$$ $$=$$ $$25 = 5^{2}$$ Weight: $$k$$ $$=$$ $$3$$ Character orbit: $$[\chi]$$ $$=$$ 25.c (of order $$4$$ and degree $$2$$) Character conductor: $$\operatorname{cond}(\chi)$$ $$=$$ $$5$$ Character field: $$\Q(i)$$ Newform subspaces: $$1$$ Sturm bound: $$7$$ Trace bound: $$0$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{3}(25, [\chi])$$.

Total New Old
Modular forms 16 8 8
Cusp forms 4 4 0
Eisenstein series 12 4 8

## Trace form

 $$4q - 12q^{6} + O(q^{10})$$ $$4q - 12q^{6} - 12q^{11} + 44q^{16} + 48q^{21} - 72q^{26} - 152q^{31} + 24q^{36} + 228q^{41} + 168q^{46} - 132q^{51} - 240q^{56} - 112q^{61} + 36q^{66} + 168q^{71} + 20q^{76} - 36q^{81} + 48q^{86} + 288q^{91} + 108q^{96} + O(q^{100})$$

## Decomposition of $$S_{3}^{\mathrm{new}}(25, [\chi])$$ into newform subspaces

Label Dim. $$A$$ Field CM Traces $q$-expansion
$$a_2$$ $$a_3$$ $$a_5$$ $$a_7$$
25.3.c.a $$4$$ $$0.681$$ $$\Q(i, \sqrt{6})$$ None $$0$$ $$0$$ $$0$$ $$0$$ $$q+\beta _{1}q^{2}+\beta _{3}q^{3}-\beta _{2}q^{4}-3q^{6}-4\beta _{1}q^{7}+\cdots$$

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