# Properties

 Label 672.1 Level 672 Weight 1 Dimension 4 Nonzero newspaces 1 Newform subspaces 2 Sturm bound 24576 Trace bound 0

## Defining parameters

 Level: $$N$$ = $$672 = 2^{5} \cdot 3 \cdot 7$$ Weight: $$k$$ = $$1$$ Nonzero newspaces: $$1$$ Newform subspaces: $$2$$ Sturm bound: $$24576$$ Trace bound: $$0$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{1}(\Gamma_1(672))$$.

Total New Old
Modular forms 840 104 736
Cusp forms 72 4 68
Eisenstein series 768 100 668

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

 $$4 q + 2 q^{7} - 2 q^{9} + O(q^{10})$$ $$4 q + 2 q^{7} - 2 q^{9} + 4 q^{15} - 2 q^{31} + 2 q^{33} - 2 q^{49} - 4 q^{55} - 4 q^{63} - 4 q^{73} - 2 q^{79} - 2 q^{81} - 2 q^{87} - 4 q^{97} + O(q^{100})$$

## Decomposition of $$S_{1}^{\mathrm{new}}(\Gamma_1(672))$$

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
672.1.d $$\chi_{672}(449, \cdot)$$ None 0 1
672.1.e $$\chi_{672}(335, \cdot)$$ None 0 1
672.1.f $$\chi_{672}(97, \cdot)$$ None 0 1
672.1.g $$\chi_{672}(463, \cdot)$$ None 0 1
672.1.l $$\chi_{672}(433, \cdot)$$ None 0 1
672.1.m $$\chi_{672}(127, \cdot)$$ None 0 1
672.1.n $$\chi_{672}(113, \cdot)$$ None 0 1
672.1.o $$\chi_{672}(671, \cdot)$$ None 0 1
672.1.r $$\chi_{672}(265, \cdot)$$ None 0 2
672.1.t $$\chi_{672}(281, \cdot)$$ None 0 2
672.1.v $$\chi_{672}(167, \cdot)$$ None 0 2
672.1.x $$\chi_{672}(295, \cdot)$$ None 0 2
672.1.z $$\chi_{672}(383, \cdot)$$ None 0 2
672.1.ba $$\chi_{672}(305, \cdot)$$ 672.1.ba.a 2 2
672.1.ba.b 2
672.1.be $$\chi_{672}(319, \cdot)$$ None 0 2
672.1.bf $$\chi_{672}(145, \cdot)$$ None 0 2
672.1.bg $$\chi_{672}(79, \cdot)$$ None 0 2
672.1.bh $$\chi_{672}(481, \cdot)$$ None 0 2
672.1.bm $$\chi_{672}(47, \cdot)$$ None 0 2
672.1.bn $$\chi_{672}(65, \cdot)$$ None 0 2
672.1.bp $$\chi_{672}(43, \cdot)$$ None 0 4
672.1.br $$\chi_{672}(83, \cdot)$$ None 0 4
672.1.bt $$\chi_{672}(13, \cdot)$$ None 0 4
672.1.bv $$\chi_{672}(29, \cdot)$$ None 0 4
672.1.bx $$\chi_{672}(151, \cdot)$$ None 0 4
672.1.bz $$\chi_{672}(215, \cdot)$$ None 0 4
672.1.cb $$\chi_{672}(137, \cdot)$$ None 0 4
672.1.cd $$\chi_{672}(73, \cdot)$$ None 0 4
672.1.ce $$\chi_{672}(53, \cdot)$$ None 0 8
672.1.cg $$\chi_{672}(61, \cdot)$$ None 0 8
672.1.ci $$\chi_{672}(59, \cdot)$$ None 0 8
672.1.ck $$\chi_{672}(67, \cdot)$$ None 0 8

## Decomposition of $$S_{1}^{\mathrm{old}}(\Gamma_1(672))$$ into lower level spaces

$$S_{1}^{\mathrm{old}}(\Gamma_1(672)) \cong$$ $$S_{1}^{\mathrm{new}}(\Gamma_1(56))$$$$^{\oplus 6}$$$$\oplus$$$$S_{1}^{\mathrm{new}}(\Gamma_1(84))$$$$^{\oplus 4}$$$$\oplus$$$$S_{1}^{\mathrm{new}}(\Gamma_1(112))$$$$^{\oplus 4}$$$$\oplus$$$$S_{1}^{\mathrm{new}}(\Gamma_1(168))$$$$^{\oplus 3}$$$$\oplus$$$$S_{1}^{\mathrm{new}}(\Gamma_1(224))$$$$^{\oplus 2}$$$$\oplus$$$$S_{1}^{\mathrm{new}}(\Gamma_1(336))$$$$^{\oplus 2}$$