Properties

 Label 63.1.d Level $63$ Weight $1$ Character orbit 63.d Rep. character $\chi_{63}(55,\cdot)$ Character field $\Q$ Dimension $1$ Newform subspaces $1$ Sturm bound $8$ Trace bound $0$

Related objects

Defining parameters

 Level: $$N$$ $$=$$ $$63 = 3^{2} \cdot 7$$ Weight: $$k$$ $$=$$ $$1$$ Character orbit: $$[\chi]$$ $$=$$ 63.d (of order $$2$$ and degree $$1$$) Character conductor: $$\operatorname{cond}(\chi)$$ $$=$$ $$7$$ Character field: $$\Q$$ Newform subspaces: $$1$$ Sturm bound: $$8$$ Trace bound: $$0$$

Dimensions

The following table gives the dimensions of various subspaces of $$M_{1}(63, [\chi])$$.

Total New Old
Modular forms 5 2 3
Cusp forms 1 1 0
Eisenstein series 4 1 3

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

 $$q - q^{4} - q^{7} + O(q^{10})$$ $$q - q^{4} - q^{7} + q^{16} + q^{25} + q^{28} - 2q^{37} - 2q^{43} + q^{49} - q^{64} + 2q^{67} + 2q^{79} + O(q^{100})$$

Decomposition of $$S_{1}^{\mathrm{new}}(63, [\chi])$$ into newform subspaces

Label Dim. $$A$$ Field Image CM RM Traces $q$-expansion
$$a_2$$ $$a_3$$ $$a_5$$ $$a_7$$
63.1.d.a $$1$$ $$0.031$$ $$\Q$$ $$D_{2}$$ $$\Q(\sqrt{-3})$$, $$\Q(\sqrt{-7})$$ $$\Q(\sqrt{21})$$ $$0$$ $$0$$ $$0$$ $$-1$$ $$q-q^{4}-q^{7}+q^{16}+q^{25}+q^{28}-2q^{37}+\cdots$$

Hecke characteristic polynomials

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