Properties

 Label 45.2.f Level 45 Weight 2 Character orbit f Rep. character $$\chi_{45}(8,\cdot)$$ Character field $$\Q(\zeta_{4})$$ Dimension 4 Newform subspaces 1 Sturm bound 12 Trace bound 0

Related objects

Defining parameters

 Level: $$N$$ = $$45 = 3^{2} \cdot 5$$ Weight: $$k$$ = $$2$$ Character orbit: $$[\chi]$$ = 45.f (of order $$4$$ and degree $$2$$) Character conductor: $$\operatorname{cond}(\chi)$$ = $$15$$ Character field: $$\Q(i)$$ Newform subspaces: $$1$$ Sturm bound: $$12$$ Trace bound: $$0$$

Dimensions

The following table gives the dimensions of various subspaces of $$M_{2}(45, [\chi])$$.

Total New Old
Modular forms 20 4 16
Cusp forms 4 4 0
Eisenstein series 16 0 16

Trace form

 $$4q - 8q^{7} + O(q^{10})$$ $$4q - 8q^{7} - 8q^{10} + 4q^{13} + 4q^{16} + 8q^{22} + 16q^{25} + 8q^{28} - 16q^{31} + 4q^{37} - 12q^{40} - 32q^{43} - 16q^{46} + 4q^{52} + 8q^{55} + 12q^{58} + 32q^{61} + 16q^{67} + 24q^{70} + 4q^{73} - 4q^{82} - 32q^{85} - 24q^{88} - 16q^{91} - 44q^{97} + O(q^{100})$$

Decomposition of $$S_{2}^{\mathrm{new}}(45, [\chi])$$ into newform subspaces

Label Dim. $$A$$ Field CM Traces $q$-expansion
$$a_2$$ $$a_3$$ $$a_5$$ $$a_7$$
45.2.f.a $$4$$ $$0.359$$ $$\Q(\zeta_{8})$$ None $$0$$ $$0$$ $$0$$ $$-8$$ $$q+\zeta_{8}q^{2}-\zeta_{8}^{2}q^{4}+(-\zeta_{8}+2\zeta_{8}^{3})q^{5}+\cdots$$

Hecke Characteristic Polynomials

$p$ $F_p(T)$
$2$ $$1 + T^{4} + 16 T^{8}$$
$3$ 
$5$ $$1 - 8 T^{2} + 25 T^{4}$$
$7$ $$( 1 + 4 T + 8 T^{2} + 28 T^{3} + 49 T^{4} )^{2}$$
$11$ $$( 1 - 6 T + 11 T^{2} )^{2}( 1 + 6 T + 11 T^{2} )^{2}$$
$13$ $$( 1 - 6 T + 13 T^{2} )^{2}( 1 + 4 T + 13 T^{2} )^{2}$$
$17$ $$1 - 254 T^{4} + 83521 T^{8}$$
$19$ $$( 1 - 19 T^{2} )^{4}$$
$23$ $$1 - 158 T^{4} + 279841 T^{8}$$
$29$ $$( 1 + 40 T^{2} + 841 T^{4} )^{2}$$
$31$ $$( 1 + 4 T + 31 T^{2} )^{4}$$
$37$ $$( 1 - 2 T + 2 T^{2} - 74 T^{3} + 1369 T^{4} )^{2}$$
$41$ $$( 1 - 80 T^{2} + 1681 T^{4} )^{2}$$
$43$ $$( 1 + 16 T + 128 T^{2} + 688 T^{3} + 1849 T^{4} )^{2}$$
$47$ $$1 - 3518 T^{4} + 4879681 T^{8}$$
$53$ $$( 1 - 56 T^{2} + 2809 T^{4} )( 1 + 56 T^{2} + 2809 T^{4} )$$
$59$ $$( 1 + 46 T^{2} + 3481 T^{4} )^{2}$$
$61$ $$( 1 - 8 T + 61 T^{2} )^{4}$$
$67$ $$( 1 - 8 T + 32 T^{2} - 536 T^{3} + 4489 T^{4} )^{2}$$
$71$ $$( 1 - 110 T^{2} + 5041 T^{4} )^{2}$$
$73$ $$( 1 - 2 T + 2 T^{2} - 146 T^{3} + 5329 T^{4} )^{2}$$
$79$ $$( 1 - 14 T^{2} + 6241 T^{4} )^{2}$$
$83$ $$1 + 8722 T^{4} + 47458321 T^{8}$$
$89$ $$( 1 + 16 T^{2} + 7921 T^{4} )^{2}$$
$97$ $$( 1 + 22 T + 242 T^{2} + 2134 T^{3} + 9409 T^{4} )^{2}$$