## Defining parameters

 Level: $$N$$ = $$155 = 5 \cdot 31$$ Weight: $$k$$ = $$1$$ Nonzero newspaces: $$1$$ Newform subspaces: $$2$$ Sturm bound: $$1920$$ Trace bound: $$0$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{1}(\Gamma_1(155))$$.

Total New Old
Modular forms 125 89 36
Cusp forms 5 3 2
Eisenstein series 120 86 34

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

$$D_n$$ $$A_4$$ $$S_4$$ $$A_5$$
Dimension 3 0 0 0

## Trace form

 $$3q - 3q^{4} - 3q^{9} + O(q^{10})$$ $$3q - 3q^{4} - 3q^{9} - 3q^{10} + 6q^{14} + 3q^{16} - 3q^{20} - 3q^{31} + 3q^{35} + 3q^{36} + 3q^{40} - 3q^{49} - 3q^{50} - 6q^{56} + 3q^{64} + 3q^{70} - 6q^{76} + 3q^{81} + 3q^{90} + 3q^{95} + O(q^{100})$$

## Decomposition of $$S_{1}^{\mathrm{new}}(\Gamma_1(155))$$

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
155.1.c $$\chi_{155}(154, \cdot)$$ 155.1.c.a 1 1
155.1.c.b 2
155.1.d $$\chi_{155}(61, \cdot)$$ None 0 1
155.1.g $$\chi_{155}(32, \cdot)$$ None 0 2
155.1.i $$\chi_{155}(99, \cdot)$$ None 0 2
155.1.k $$\chi_{155}(6, \cdot)$$ None 0 2
155.1.l $$\chi_{155}(46, \cdot)$$ None 0 4
155.1.m $$\chi_{155}(29, \cdot)$$ None 0 4
155.1.o $$\chi_{155}(67, \cdot)$$ None 0 4
155.1.s $$\chi_{155}(2, \cdot)$$ None 0 8
155.1.t $$\chi_{155}(11, \cdot)$$ None 0 8
155.1.v $$\chi_{155}(24, \cdot)$$ None 0 8
155.1.w $$\chi_{155}(7, \cdot)$$ None 0 16

## Decomposition of $$S_{1}^{\mathrm{old}}(\Gamma_1(155))$$ into lower level spaces

$$S_{1}^{\mathrm{old}}(\Gamma_1(155)) \cong$$ $$S_{1}^{\mathrm{new}}(\Gamma_1(31))$$$$^{\oplus 2}$$

## Hecke characteristic polynomials

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