Properties

 Label 240.1 Level 240 Weight 1 Dimension 4 Nonzero newspaces 1 Newform subspaces 1 Sturm bound 3072 Trace bound 0

Defining parameters

 Level: $$N$$ = $$240\( 240 = 2^{4} \cdot 3 \cdot 5$$ \) Weight: $$k$$ = $$1$$ Nonzero newspaces: $$1$$ Newform subspaces: $$1$$ Sturm bound: $$3072$$ Trace bound: $$0$$

Dimensions

The following table gives the dimensions of various subspaces of $$M_{1}(\Gamma_1(240))$$.

Total New Old
Modular forms 234 30 204
Cusp forms 10 4 6
Eisenstein series 224 26 198

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

$$D_n$$ $$A_4$$ $$S_4$$ $$A_5$$
Dimension 4 0 0 0

Trace form

 $$4q + O(q^{10})$$ $$4q + 4q^{10} - 4q^{15} - 4q^{16} - 4q^{19} + 4q^{24} - 4q^{34} - 4q^{36} - 4q^{46} - 4q^{49} + 4q^{51} + 4q^{54} + 4q^{61} + 4q^{69} + 4q^{76} + 8q^{79} - 4q^{81} - 4q^{85} + 4q^{94} + O(q^{100})$$

Decomposition of $$S_{1}^{\mathrm{new}}(\Gamma_1(240))$$

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
240.1.c $$\chi_{240}(209, \cdot)$$ None 0 1
240.1.e $$\chi_{240}(31, \cdot)$$ None 0 1
240.1.g $$\chi_{240}(151, \cdot)$$ None 0 1
240.1.i $$\chi_{240}(89, \cdot)$$ None 0 1
240.1.j $$\chi_{240}(79, \cdot)$$ None 0 1
240.1.l $$\chi_{240}(161, \cdot)$$ None 0 1
240.1.n $$\chi_{240}(41, \cdot)$$ None 0 1
240.1.p $$\chi_{240}(199, \cdot)$$ None 0 1
240.1.q $$\chi_{240}(19, \cdot)$$ None 0 2
240.1.r $$\chi_{240}(101, \cdot)$$ None 0 2
240.1.u $$\chi_{240}(23, \cdot)$$ None 0 2
240.1.x $$\chi_{240}(73, \cdot)$$ None 0 2
240.1.z $$\chi_{240}(83, \cdot)$$ None 0 2
240.1.ba $$\chi_{240}(13, \cdot)$$ None 0 2
240.1.bd $$\chi_{240}(203, \cdot)$$ None 0 2
240.1.be $$\chi_{240}(133, \cdot)$$ None 0 2
240.1.bg $$\chi_{240}(97, \cdot)$$ None 0 2
240.1.bj $$\chi_{240}(47, \cdot)$$ None 0 2
240.1.bm $$\chi_{240}(29, \cdot)$$ 240.1.bm.a 4 2
240.1.bn $$\chi_{240}(91, \cdot)$$ None 0 2

Decomposition of $$S_{1}^{\mathrm{old}}(\Gamma_1(240))$$ into lower level spaces

$$S_{1}^{\mathrm{old}}(\Gamma_1(240)) \cong$$ $$S_{1}^{\mathrm{new}}(\Gamma_1(80))$$$$^{\oplus 2}$$$$\oplus$$$$S_{1}^{\mathrm{new}}(\Gamma_1(120))$$$$^{\oplus 2}$$

Hecke characteristic polynomials

$p$ $F_p(T)$
$2$ $$1 + T^{4}$$
$3$ $$1 + T^{4}$$
$5$ $$1 + T^{4}$$
$7$ $$( 1 + T^{2} )^{4}$$
$11$ $$( 1 + T^{4} )^{2}$$
$13$ $$( 1 + T^{4} )^{2}$$
$17$ $$( 1 + T^{4} )^{2}$$
$19$ $$( 1 + T )^{4}( 1 + T^{2} )^{2}$$
$23$ $$( 1 + T^{4} )^{2}$$
$29$ $$( 1 + T^{4} )^{2}$$
$31$ $$( 1 + T^{2} )^{4}$$
$37$ $$( 1 + T^{4} )^{2}$$
$41$ $$( 1 + T^{2} )^{4}$$
$43$ $$( 1 + T^{4} )^{2}$$
$47$ $$( 1 + T^{4} )^{2}$$
$53$ $$( 1 + T^{4} )^{2}$$
$59$ $$( 1 + T^{4} )^{2}$$
$61$ $$( 1 - T )^{4}( 1 + T^{2} )^{2}$$
$67$ $$( 1 + T^{4} )^{2}$$
$71$ $$( 1 + T^{2} )^{4}$$
$73$ $$( 1 + T^{2} )^{4}$$
$79$ $$( 1 - T )^{8}$$
$83$ $$( 1 + T^{4} )^{2}$$
$89$ $$( 1 + T^{2} )^{4}$$
$97$ $$( 1 - T )^{4}( 1 + T )^{4}$$