# Properties

 Label 3240.1 Level 3240 Weight 1 Dimension 108 Nonzero newspaces 7 Newform subspaces 35 Sturm bound 559872 Trace bound 19

## Defining parameters

 Level: $$N$$ = $$3240 = 2^{3} \cdot 3^{4} \cdot 5$$ Weight: $$k$$ = $$1$$ Nonzero newspaces: $$7$$ Newform subspaces: $$35$$ Sturm bound: $$559872$$ Trace bound: $$19$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{1}(\Gamma_1(3240))$$.

Total New Old
Modular forms 5938 780 5158
Cusp forms 754 108 646
Eisenstein series 5184 672 4512

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

$$D_n$$ $$A_4$$ $$S_4$$ $$A_5$$
Dimension 88 0 20 0

## Trace form

 $$108 q + O(q^{10})$$ $$108 q - 4 q^{10} + 4 q^{16} + 8 q^{19} - 6 q^{25} + 16 q^{34} + 12 q^{37} + 10 q^{40} - 8 q^{46} + 4 q^{49} - 24 q^{55} + 12 q^{58} + 4 q^{61} + 24 q^{64} + 6 q^{70} - 32 q^{91} + 4 q^{94} + O(q^{100})$$

## Decomposition of $$S_{1}^{\mathrm{new}}(\Gamma_1(3240))$$

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 available newforms together with their dimension.

Label $$\chi$$ Newforms Dimension $$\chi$$ degree
3240.1.c $$\chi_{3240}(809, \cdot)$$ None 0 1
3240.1.e $$\chi_{3240}(2431, \cdot)$$ None 0 1
3240.1.g $$\chi_{3240}(811, \cdot)$$ None 0 1
3240.1.i $$\chi_{3240}(2429, \cdot)$$ None 0 1
3240.1.j $$\chi_{3240}(3079, \cdot)$$ None 0 1
3240.1.l $$\chi_{3240}(161, \cdot)$$ None 0 1
3240.1.n $$\chi_{3240}(1781, \cdot)$$ None 0 1
3240.1.p $$\chi_{3240}(1459, \cdot)$$ 3240.1.p.a 1 1
3240.1.p.b 1
3240.1.p.c 1
3240.1.p.d 1
3240.1.p.e 2
3240.1.p.f 2
3240.1.r $$\chi_{3240}(323, \cdot)$$ None 0 2
3240.1.u $$\chi_{3240}(973, \cdot)$$ None 0 2
3240.1.v $$\chi_{3240}(1297, \cdot)$$ 3240.1.v.a 2 2
3240.1.v.b 2
3240.1.y $$\chi_{3240}(647, \cdot)$$ None 0 2
3240.1.z $$\chi_{3240}(379, \cdot)$$ 3240.1.z.a 2 2
3240.1.z.b 2
3240.1.z.c 2
3240.1.z.d 2
3240.1.z.e 2
3240.1.z.f 2
3240.1.z.g 2
3240.1.z.h 2
3240.1.z.i 2
3240.1.z.j 2
3240.1.z.k 4
3240.1.z.l 4
3240.1.ba $$\chi_{3240}(701, \cdot)$$ None 0 2
3240.1.bc $$\chi_{3240}(1241, \cdot)$$ None 0 2
3240.1.be $$\chi_{3240}(919, \cdot)$$ None 0 2
3240.1.bh $$\chi_{3240}(269, \cdot)$$ 3240.1.bh.a 2 2
3240.1.bh.b 2
3240.1.bh.c 2
3240.1.bh.d 2
3240.1.bh.e 4
3240.1.bh.f 4
3240.1.bh.g 4
3240.1.bh.h 4
3240.1.bh.i 4
3240.1.bj $$\chi_{3240}(1891, \cdot)$$ None 0 2
3240.1.bl $$\chi_{3240}(271, \cdot)$$ None 0 2
3240.1.bn $$\chi_{3240}(1889, \cdot)$$ 3240.1.bn.a 8 2
3240.1.bq $$\chi_{3240}(217, \cdot)$$ 3240.1.bq.a 4 4
3240.1.bq.b 4
3240.1.br $$\chi_{3240}(863, \cdot)$$ None 0 4
3240.1.bu $$\chi_{3240}(107, \cdot)$$ None 0 4
3240.1.bv $$\chi_{3240}(757, \cdot)$$ 3240.1.bv.a 8 4
3240.1.bv.b 8
3240.1.bv.c 8
3240.1.by $$\chi_{3240}(91, \cdot)$$ None 0 6
3240.1.bz $$\chi_{3240}(89, \cdot)$$ None 0 6
3240.1.ca $$\chi_{3240}(629, \cdot)$$ None 0 6
3240.1.cb $$\chi_{3240}(631, \cdot)$$ None 0 6
3240.1.ce $$\chi_{3240}(521, \cdot)$$ None 0 6
3240.1.cf $$\chi_{3240}(19, \cdot)$$ None 0 6
3240.1.ck $$\chi_{3240}(199, \cdot)$$ None 0 6
3240.1.cl $$\chi_{3240}(341, \cdot)$$ None 0 6
3240.1.cn $$\chi_{3240}(143, \cdot)$$ None 0 12
3240.1.co $$\chi_{3240}(37, \cdot)$$ None 0 12
3240.1.cr $$\chi_{3240}(467, \cdot)$$ None 0 12
3240.1.cs $$\chi_{3240}(73, \cdot)$$ None 0 12
3240.1.cv $$\chi_{3240}(209, \cdot)$$ None 0 18
3240.1.cw $$\chi_{3240}(101, \cdot)$$ None 0 18
3240.1.cz $$\chi_{3240}(31, \cdot)$$ None 0 18
3240.1.db $$\chi_{3240}(139, \cdot)$$ None 0 18
3240.1.dd $$\chi_{3240}(79, \cdot)$$ None 0 18
3240.1.df $$\chi_{3240}(211, \cdot)$$ None 0 18
3240.1.dg $$\chi_{3240}(41, \cdot)$$ None 0 18
3240.1.di $$\chi_{3240}(29, \cdot)$$ None 0 18
3240.1.dl $$\chi_{3240}(83, \cdot)$$ None 0 36
3240.1.dm $$\chi_{3240}(13, \cdot)$$ None 0 36
3240.1.dp $$\chi_{3240}(23, \cdot)$$ None 0 36
3240.1.dq $$\chi_{3240}(97, \cdot)$$ None 0 36

## Decomposition of $$S_{1}^{\mathrm{old}}(\Gamma_1(3240))$$ into lower level spaces

$$S_{1}^{\mathrm{old}}(\Gamma_1(3240)) \cong$$ $$S_{1}^{\mathrm{new}}(\Gamma_1(1))$$$$^{\oplus 40}$$$$\oplus$$$$S_{1}^{\mathrm{new}}(\Gamma_1(2))$$$$^{\oplus 30}$$$$\oplus$$$$S_{1}^{\mathrm{new}}(\Gamma_1(3))$$$$^{\oplus 32}$$$$\oplus$$$$S_{1}^{\mathrm{new}}(\Gamma_1(4))$$$$^{\oplus 20}$$$$\oplus$$$$S_{1}^{\mathrm{new}}(\Gamma_1(5))$$$$^{\oplus 20}$$$$\oplus$$$$S_{1}^{\mathrm{new}}(\Gamma_1(6))$$$$^{\oplus 24}$$$$\oplus$$$$S_{1}^{\mathrm{new}}(\Gamma_1(8))$$$$^{\oplus 10}$$$$\oplus$$$$S_{1}^{\mathrm{new}}(\Gamma_1(9))$$$$^{\oplus 24}$$$$\oplus$$$$S_{1}^{\mathrm{new}}(\Gamma_1(10))$$$$^{\oplus 15}$$$$\oplus$$$$S_{1}^{\mathrm{new}}(\Gamma_1(12))$$$$^{\oplus 16}$$$$\oplus$$$$S_{1}^{\mathrm{new}}(\Gamma_1(15))$$$$^{\oplus 16}$$$$\oplus$$$$S_{1}^{\mathrm{new}}(\Gamma_1(18))$$$$^{\oplus 18}$$$$\oplus$$$$S_{1}^{\mathrm{new}}(\Gamma_1(20))$$$$^{\oplus 10}$$$$\oplus$$$$S_{1}^{\mathrm{new}}(\Gamma_1(24))$$$$^{\oplus 8}$$$$\oplus$$$$S_{1}^{\mathrm{new}}(\Gamma_1(27))$$$$^{\oplus 16}$$$$\oplus$$$$S_{1}^{\mathrm{new}}(\Gamma_1(30))$$$$^{\oplus 12}$$$$\oplus$$$$S_{1}^{\mathrm{new}}(\Gamma_1(36))$$$$^{\oplus 12}$$$$\oplus$$$$S_{1}^{\mathrm{new}}(\Gamma_1(40))$$$$^{\oplus 5}$$$$\oplus$$$$S_{1}^{\mathrm{new}}(\Gamma_1(45))$$$$^{\oplus 12}$$$$\oplus$$$$S_{1}^{\mathrm{new}}(\Gamma_1(54))$$$$^{\oplus 12}$$$$\oplus$$$$S_{1}^{\mathrm{new}}(\Gamma_1(60))$$$$^{\oplus 8}$$$$\oplus$$$$S_{1}^{\mathrm{new}}(\Gamma_1(72))$$$$^{\oplus 6}$$$$\oplus$$$$S_{1}^{\mathrm{new}}(\Gamma_1(81))$$$$^{\oplus 8}$$$$\oplus$$$$S_{1}^{\mathrm{new}}(\Gamma_1(90))$$$$^{\oplus 9}$$$$\oplus$$$$S_{1}^{\mathrm{new}}(\Gamma_1(108))$$$$^{\oplus 8}$$$$\oplus$$$$S_{1}^{\mathrm{new}}(\Gamma_1(120))$$$$^{\oplus 4}$$$$\oplus$$$$S_{1}^{\mathrm{new}}(\Gamma_1(135))$$$$^{\oplus 8}$$$$\oplus$$$$S_{1}^{\mathrm{new}}(\Gamma_1(162))$$$$^{\oplus 6}$$$$\oplus$$$$S_{1}^{\mathrm{new}}(\Gamma_1(180))$$$$^{\oplus 6}$$$$\oplus$$$$S_{1}^{\mathrm{new}}(\Gamma_1(216))$$$$^{\oplus 4}$$$$\oplus$$$$S_{1}^{\mathrm{new}}(\Gamma_1(270))$$$$^{\oplus 6}$$$$\oplus$$$$S_{1}^{\mathrm{new}}(\Gamma_1(324))$$$$^{\oplus 4}$$$$\oplus$$$$S_{1}^{\mathrm{new}}(\Gamma_1(360))$$$$^{\oplus 3}$$$$\oplus$$$$S_{1}^{\mathrm{new}}(\Gamma_1(405))$$$$^{\oplus 4}$$$$\oplus$$$$S_{1}^{\mathrm{new}}(\Gamma_1(540))$$$$^{\oplus 4}$$$$\oplus$$$$S_{1}^{\mathrm{new}}(\Gamma_1(648))$$$$^{\oplus 2}$$$$\oplus$$$$S_{1}^{\mathrm{new}}(\Gamma_1(810))$$$$^{\oplus 3}$$$$\oplus$$$$S_{1}^{\mathrm{new}}(\Gamma_1(1080))$$$$^{\oplus 2}$$$$\oplus$$$$S_{1}^{\mathrm{new}}(\Gamma_1(1620))$$$$^{\oplus 2}$$$$\oplus$$$$S_{1}^{\mathrm{new}}(\Gamma_1(3240))$$$$^{\oplus 1}$$