## Defining parameters

 Level: $$N$$ = $$23$$ Weight: $$k$$ = $$1$$ Nonzero newspaces: $$1$$ Newform subspaces: $$1$$ Sturm bound: $$44$$ Trace bound: $$0$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{1}(\Gamma_1(23))$$.

Total New Old
Modular forms 12 12 0
Cusp forms 1 1 0
Eisenstein series 11 11 0

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

 $$q - q^{2} - q^{3} + q^{6} + q^{8} + O(q^{10})$$ $$q - q^{2} - q^{3} + q^{6} + q^{8} - q^{13} - q^{16} + q^{23} - q^{24} + q^{25} + q^{26} + q^{27} - q^{29} - q^{31} + q^{39} - q^{41} - q^{46} - q^{47} + q^{48} + q^{49} - q^{50} - q^{54} + q^{58} + 2q^{59} + q^{62} + q^{64} - q^{69} - q^{71} - q^{73} - q^{75} - q^{78} - q^{81} + q^{82} + q^{87} + q^{93} + q^{94} - q^{98} + O(q^{100})$$

## Decomposition of $$S_{1}^{\mathrm{new}}(\Gamma_1(23))$$

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
23.1.b $$\chi_{23}(22, \cdot)$$ 23.1.b.a 1 1
23.1.d $$\chi_{23}(5, \cdot)$$ None 0 10

## Hecke Characteristic Polynomials

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