# Properties

 Label 108.1.c Level 108 Weight 1 Character orbit c Rep. character $$\chi_{108}(53,\cdot)$$ Character field $$\Q$$ Dimension 1 Newform subspaces 1 Sturm bound 18 Trace bound 0

# Related objects

## Defining parameters

 Level: $$N$$ $$=$$ $$108 = 2^{2} \cdot 3^{3}$$ Weight: $$k$$ $$=$$ $$1$$ Character orbit: $$[\chi]$$ $$=$$ 108.c (of order $$2$$ and degree $$1$$) Character conductor: $$\operatorname{cond}(\chi)$$ $$=$$ $$3$$ Character field: $$\Q$$ Newform subspaces: $$1$$ Sturm bound: $$18$$ Trace bound: $$0$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{1}(108, [\chi])$$.

Total New Old
Modular forms 10 1 9
Cusp forms 1 1 0
Eisenstein series 9 0 9

The following table gives the dimensions of subspaces with specified projective image type.

$$D_n$$ $$A_4$$ $$S_4$$ $$A_5$$
Dimension 1 0 0 0

## Trace form

 $$q - q^{7} + O(q^{10})$$ $$q - q^{7} - q^{13} - q^{19} + q^{25} + 2q^{31} - q^{37} + 2q^{43} - q^{61} - q^{67} - q^{73} - q^{79} + q^{91} - q^{97} + O(q^{100})$$

## Decomposition of $$S_{1}^{\mathrm{new}}(108, [\chi])$$ into newform subspaces

Label Dim. $$A$$ Field Image CM RM Traces $q$-expansion
$$a_2$$ $$a_3$$ $$a_5$$ $$a_7$$
108.1.c.a $$1$$ $$0.054$$ $$\Q$$ $$D_{3}$$ $$\Q(\sqrt{-3})$$ None $$0$$ $$0$$ $$0$$ $$-1$$ $$q-q^{7}-q^{13}-q^{19}+q^{25}+2q^{31}+\cdots$$

## Hecke characteristic polynomials

$p$ $F_p(T)$
$2$ 1
$3$ 1
$5$ $$( 1 - T )( 1 + T )$$
$7$ $$1 + T + T^{2}$$
$11$ $$( 1 - T )( 1 + T )$$
$13$ $$1 + T + T^{2}$$
$17$ $$( 1 - T )( 1 + T )$$
$19$ $$1 + T + T^{2}$$
$23$ $$( 1 - T )( 1 + T )$$
$29$ $$( 1 - T )( 1 + T )$$
$31$ $$( 1 - T )^{2}$$
$37$ $$1 + T + T^{2}$$
$41$ $$( 1 - T )( 1 + T )$$
$43$ $$( 1 - T )^{2}$$
$47$ $$( 1 - T )( 1 + T )$$
$53$ $$( 1 - T )( 1 + T )$$
$59$ $$( 1 - T )( 1 + T )$$
$61$ $$1 + T + T^{2}$$
$67$ $$1 + T + T^{2}$$
$71$ $$( 1 - T )( 1 + T )$$
$73$ $$1 + T + T^{2}$$
$79$ $$1 + T + T^{2}$$
$83$ $$( 1 - T )( 1 + T )$$
$89$ $$( 1 - T )( 1 + T )$$
$97$ $$1 + T + T^{2}$$