# Properties

 Label 1344.1 Level 1344 Weight 1 Dimension 42 Nonzero newspaces 6 Newform subspaces 16 Sturm bound 98304 Trace bound 13

## Defining parameters

 Level: $$N$$ = $$1344 = 2^{6} \cdot 3 \cdot 7$$ Weight: $$k$$ = $$1$$ Nonzero newspaces: $$6$$ Newform subspaces: $$16$$ Sturm bound: $$98304$$ Trace bound: $$13$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{1}(\Gamma_1(1344))$$.

Total New Old
Modular forms 1916 262 1654
Cusp forms 188 42 146
Eisenstein series 1728 220 1508

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

$$D_n$$ $$A_4$$ $$S_4$$ $$A_5$$
Dimension 42 0 0 0

## Trace form

 $$42q + 2q^{9} + O(q^{10})$$ $$42q + 2q^{9} + 4q^{13} + 2q^{21} - 10q^{25} - 12q^{33} + 4q^{37} + 2q^{49} - 12q^{57} + 4q^{61} - 12q^{73} - 6q^{81} - 8q^{93} - 8q^{97} + O(q^{100})$$

## Decomposition of $$S_{1}^{\mathrm{new}}(\Gamma_1(1344))$$

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
1344.1.d $$\chi_{1344}(449, \cdot)$$ None 0 1
1344.1.e $$\chi_{1344}(671, \cdot)$$ 1344.1.e.a 2 1
1344.1.e.b 2
1344.1.e.c 2
1344.1.e.d 2
1344.1.f $$\chi_{1344}(769, \cdot)$$ None 0 1
1344.1.g $$\chi_{1344}(799, \cdot)$$ None 0 1
1344.1.l $$\chi_{1344}(97, \cdot)$$ None 0 1
1344.1.m $$\chi_{1344}(127, \cdot)$$ None 0 1
1344.1.n $$\chi_{1344}(1121, \cdot)$$ None 0 1
1344.1.o $$\chi_{1344}(1343, \cdot)$$ 1344.1.o.a 1 1
1344.1.o.b 1
1344.1.r $$\chi_{1344}(433, \cdot)$$ None 0 2
1344.1.t $$\chi_{1344}(113, \cdot)$$ None 0 2
1344.1.v $$\chi_{1344}(335, \cdot)$$ None 0 2
1344.1.x $$\chi_{1344}(463, \cdot)$$ None 0 2
1344.1.z $$\chi_{1344}(383, \cdot)$$ 1344.1.z.a 2 2
1344.1.z.b 2
1344.1.ba $$\chi_{1344}(737, \cdot)$$ 1344.1.ba.a 4 2
1344.1.ba.b 4
1344.1.be $$\chi_{1344}(319, \cdot)$$ None 0 2
1344.1.bf $$\chi_{1344}(481, \cdot)$$ None 0 2
1344.1.bg $$\chi_{1344}(415, \cdot)$$ None 0 2
1344.1.bh $$\chi_{1344}(577, \cdot)$$ None 0 2
1344.1.bm $$\chi_{1344}(479, \cdot)$$ 1344.1.bm.a 4 2
1344.1.bm.b 4
1344.1.bm.c 4
1344.1.bm.d 4
1344.1.bn $$\chi_{1344}(65, \cdot)$$ 1344.1.bn.a 2 2
1344.1.bn.b 2
1344.1.bp $$\chi_{1344}(295, \cdot)$$ None 0 4
1344.1.br $$\chi_{1344}(167, \cdot)$$ None 0 4
1344.1.bt $$\chi_{1344}(265, \cdot)$$ None 0 4
1344.1.bv $$\chi_{1344}(281, \cdot)$$ None 0 4
1344.1.bx $$\chi_{1344}(79, \cdot)$$ None 0 4
1344.1.bz $$\chi_{1344}(47, \cdot)$$ None 0 4
1344.1.cb $$\chi_{1344}(305, \cdot)$$ None 0 4
1344.1.cd $$\chi_{1344}(145, \cdot)$$ None 0 4
1344.1.ce $$\chi_{1344}(83, \cdot)$$ None 0 8
1344.1.cf $$\chi_{1344}(29, \cdot)$$ None 0 8
1344.1.ck $$\chi_{1344}(13, \cdot)$$ None 0 8
1344.1.cl $$\chi_{1344}(43, \cdot)$$ None 0 8
1344.1.cm $$\chi_{1344}(137, \cdot)$$ None 0 8
1344.1.co $$\chi_{1344}(73, \cdot)$$ None 0 8
1344.1.cq $$\chi_{1344}(215, \cdot)$$ None 0 8
1344.1.cs $$\chi_{1344}(151, \cdot)$$ None 0 8
1344.1.cu $$\chi_{1344}(67, \cdot)$$ None 0 16
1344.1.cv $$\chi_{1344}(61, \cdot)$$ None 0 16
1344.1.da $$\chi_{1344}(53, \cdot)$$ None 0 16
1344.1.db $$\chi_{1344}(59, \cdot)$$ None 0 16

## Decomposition of $$S_{1}^{\mathrm{old}}(\Gamma_1(1344))$$ into lower level spaces

$$S_{1}^{\mathrm{old}}(\Gamma_1(1344)) \cong$$ $$S_{1}^{\mathrm{new}}(\Gamma_1(56))$$$$^{\oplus 8}$$$$\oplus$$$$S_{1}^{\mathrm{new}}(\Gamma_1(84))$$$$^{\oplus 5}$$$$\oplus$$$$S_{1}^{\mathrm{new}}(\Gamma_1(112))$$$$^{\oplus 6}$$$$\oplus$$$$S_{1}^{\mathrm{new}}(\Gamma_1(168))$$$$^{\oplus 4}$$$$\oplus$$$$S_{1}^{\mathrm{new}}(\Gamma_1(192))$$$$^{\oplus 2}$$$$\oplus$$$$S_{1}^{\mathrm{new}}(\Gamma_1(224))$$$$^{\oplus 4}$$$$\oplus$$$$S_{1}^{\mathrm{new}}(\Gamma_1(336))$$$$^{\oplus 3}$$$$\oplus$$$$S_{1}^{\mathrm{new}}(\Gamma_1(448))$$$$^{\oplus 2}$$$$\oplus$$$$S_{1}^{\mathrm{new}}(\Gamma_1(672))$$$$^{\oplus 2}$$