# Properties

 Label 3040.1 Level 3040 Weight 1 Dimension 56 Nonzero newspaces 4 Newform subspaces 6 Sturm bound 552960 Trace bound 1

## Defining parameters

 Level: $$N$$ = $$3040 = 2^{5} \cdot 5 \cdot 19$$ Weight: $$k$$ = $$1$$ Nonzero newspaces: $$4$$ Newform subspaces: $$6$$ Sturm bound: $$552960$$ Trace bound: $$1$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{1}(\Gamma_1(3040))$$.

Total New Old
Modular forms 5016 1076 3940
Cusp forms 408 56 352
Eisenstein series 4608 1020 3588

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

$$D_n$$ $$A_4$$ $$S_4$$ $$A_5$$
Dimension 56 0 0 0

## Trace form

 $$56 q - 10 q^{9} + O(q^{10})$$ $$56 q - 10 q^{9} + 4 q^{11} + 2 q^{19} - 10 q^{25} + 4 q^{35} - 4 q^{41} + 2 q^{49} + 4 q^{59} + 14 q^{65} - 32 q^{66} + 32 q^{80} + 6 q^{81} + 14 q^{89} + 8 q^{91} - 40 q^{95} - 32 q^{96} - 28 q^{99} + O(q^{100})$$

## Decomposition of $$S_{1}^{\mathrm{new}}(\Gamma_1(3040))$$

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
3040.1.b $$\chi_{3040}(1329, \cdot)$$ 3040.1.b.a 8 1
3040.1.c $$\chi_{3040}(191, \cdot)$$ None 0 1
3040.1.h $$\chi_{3040}(2241, \cdot)$$ None 0 1
3040.1.i $$\chi_{3040}(2319, \cdot)$$ None 0 1
3040.1.l $$\chi_{3040}(1711, \cdot)$$ None 0 1
3040.1.m $$\chi_{3040}(2849, \cdot)$$ None 0 1
3040.1.n $$\chi_{3040}(799, \cdot)$$ None 0 1
3040.1.o $$\chi_{3040}(721, \cdot)$$ None 0 1
3040.1.s $$\chi_{3040}(1673, \cdot)$$ None 0 2
3040.1.u $$\chi_{3040}(2583, \cdot)$$ None 0 2
3040.1.v $$\chi_{3040}(39, \cdot)$$ None 0 2
3040.1.x $$\chi_{3040}(1481, \cdot)$$ None 0 2
3040.1.z $$\chi_{3040}(913, \cdot)$$ None 0 2
3040.1.ba $$\chi_{3040}(607, \cdot)$$ None 0 2
3040.1.bf $$\chi_{3040}(1217, \cdot)$$ None 0 2
3040.1.bg $$\chi_{3040}(303, \cdot)$$ None 0 2
3040.1.bh $$\chi_{3040}(569, \cdot)$$ None 0 2
3040.1.bj $$\chi_{3040}(951, \cdot)$$ None 0 2
3040.1.bm $$\chi_{3040}(1063, \cdot)$$ None 0 2
3040.1.bo $$\chi_{3040}(153, \cdot)$$ None 0 2
3040.1.br $$\chi_{3040}(449, \cdot)$$ None 0 2
3040.1.bs $$\chi_{3040}(1071, \cdot)$$ None 0 2
3040.1.bt $$\chi_{3040}(1361, \cdot)$$ None 0 2
3040.1.bu $$\chi_{3040}(159, \cdot)$$ None 0 2
3040.1.bw $$\chi_{3040}(1151, \cdot)$$ None 0 2
3040.1.bx $$\chi_{3040}(369, \cdot)$$ None 0 2
3040.1.cc $$\chi_{3040}(239, \cdot)$$ 3040.1.cc.a 2 2
3040.1.cc.b 2
3040.1.cd $$\chi_{3040}(1281, \cdot)$$ None 0 2
3040.1.cg $$\chi_{3040}(837, \cdot)$$ None 0 4
3040.1.ch $$\chi_{3040}(227, \cdot)$$ None 0 4
3040.1.ci $$\chi_{3040}(341, \cdot)$$ None 0 4
3040.1.cj $$\chi_{3040}(571, \cdot)$$ None 0 4
3040.1.cm $$\chi_{3040}(419, \cdot)$$ None 0 4
3040.1.cn $$\chi_{3040}(189, \cdot)$$ 3040.1.cn.a 32 4
3040.1.cs $$\chi_{3040}(987, \cdot)$$ None 0 4
3040.1.ct $$\chi_{3040}(77, \cdot)$$ None 0 4
3040.1.cw $$\chi_{3040}(1113, \cdot)$$ None 0 4
3040.1.cy $$\chi_{3040}(103, \cdot)$$ None 0 4
3040.1.cz $$\chi_{3040}(521, \cdot)$$ None 0 4
3040.1.db $$\chi_{3040}(919, \cdot)$$ None 0 4
3040.1.df $$\chi_{3040}(273, \cdot)$$ None 0 4
3040.1.dg $$\chi_{3040}(863, \cdot)$$ None 0 4
3040.1.dh $$\chi_{3040}(353, \cdot)$$ None 0 4
3040.1.di $$\chi_{3040}(943, \cdot)$$ None 0 4
3040.1.dl $$\chi_{3040}(311, \cdot)$$ None 0 4
3040.1.dn $$\chi_{3040}(1129, \cdot)$$ None 0 4
3040.1.dq $$\chi_{3040}(183, \cdot)$$ None 0 4
3040.1.ds $$\chi_{3040}(1033, \cdot)$$ None 0 4
3040.1.du $$\chi_{3040}(641, \cdot)$$ None 0 6
3040.1.dv $$\chi_{3040}(719, \cdot)$$ 3040.1.dv.a 6 6
3040.1.dv.b 6
3040.1.dw $$\chi_{3040}(479, \cdot)$$ None 0 6
3040.1.dx $$\chi_{3040}(241, \cdot)$$ None 0 6
3040.1.ea $$\chi_{3040}(111, \cdot)$$ None 0 6
3040.1.eb $$\chi_{3040}(129, \cdot)$$ None 0 6
3040.1.eg $$\chi_{3040}(849, \cdot)$$ None 0 6
3040.1.eh $$\chi_{3040}(351, \cdot)$$ None 0 6
3040.1.ek $$\chi_{3040}(787, \cdot)$$ None 0 8
3040.1.el $$\chi_{3040}(197, \cdot)$$ None 0 8
3040.1.em $$\chi_{3040}(69, \cdot)$$ None 0 8
3040.1.en $$\chi_{3040}(539, \cdot)$$ None 0 8
3040.1.eq $$\chi_{3040}(11, \cdot)$$ None 0 8
3040.1.er $$\chi_{3040}(141, \cdot)$$ None 0 8
3040.1.ew $$\chi_{3040}(957, \cdot)$$ None 0 8
3040.1.ex $$\chi_{3040}(27, \cdot)$$ None 0 8
3040.1.fa $$\chi_{3040}(89, \cdot)$$ None 0 12
3040.1.fb $$\chi_{3040}(631, \cdot)$$ None 0 12
3040.1.fc $$\chi_{3040}(833, \cdot)$$ None 0 12
3040.1.fd $$\chi_{3040}(143, \cdot)$$ None 0 12
3040.1.fg $$\chi_{3040}(583, \cdot)$$ None 0 12
3040.1.fh $$\chi_{3040}(137, \cdot)$$ None 0 12
3040.1.fk $$\chi_{3040}(73, \cdot)$$ None 0 12
3040.1.fl $$\chi_{3040}(167, \cdot)$$ None 0 12
3040.1.fo $$\chi_{3040}(17, \cdot)$$ None 0 12
3040.1.fp $$\chi_{3040}(127, \cdot)$$ None 0 12
3040.1.fu $$\chi_{3040}(41, \cdot)$$ None 0 12
3040.1.fv $$\chi_{3040}(119, \cdot)$$ None 0 12
3040.1.fw $$\chi_{3040}(3, \cdot)$$ None 0 24
3040.1.fx $$\chi_{3040}(157, \cdot)$$ None 0 24
3040.1.ge $$\chi_{3040}(29, \cdot)$$ None 0 24
3040.1.gf $$\chi_{3040}(131, \cdot)$$ None 0 24
3040.1.gg $$\chi_{3040}(21, \cdot)$$ None 0 24
3040.1.gh $$\chi_{3040}(99, \cdot)$$ None 0 24
3040.1.gi $$\chi_{3040}(93, \cdot)$$ None 0 24
3040.1.gj $$\chi_{3040}(67, \cdot)$$ None 0 24

## Decomposition of $$S_{1}^{\mathrm{old}}(\Gamma_1(3040))$$ into lower level spaces

$$S_{1}^{\mathrm{old}}(\Gamma_1(3040)) \cong$$ $$S_{1}^{\mathrm{new}}(\Gamma_1(1))$$$$^{\oplus 24}$$$$\oplus$$$$S_{1}^{\mathrm{new}}(\Gamma_1(2))$$$$^{\oplus 20}$$$$\oplus$$$$S_{1}^{\mathrm{new}}(\Gamma_1(4))$$$$^{\oplus 16}$$$$\oplus$$$$S_{1}^{\mathrm{new}}(\Gamma_1(5))$$$$^{\oplus 12}$$$$\oplus$$$$S_{1}^{\mathrm{new}}(\Gamma_1(8))$$$$^{\oplus 12}$$$$\oplus$$$$S_{1}^{\mathrm{new}}(\Gamma_1(10))$$$$^{\oplus 10}$$$$\oplus$$$$S_{1}^{\mathrm{new}}(\Gamma_1(16))$$$$^{\oplus 8}$$$$\oplus$$$$S_{1}^{\mathrm{new}}(\Gamma_1(19))$$$$^{\oplus 12}$$$$\oplus$$$$S_{1}^{\mathrm{new}}(\Gamma_1(20))$$$$^{\oplus 8}$$$$\oplus$$$$S_{1}^{\mathrm{new}}(\Gamma_1(32))$$$$^{\oplus 4}$$$$\oplus$$$$S_{1}^{\mathrm{new}}(\Gamma_1(38))$$$$^{\oplus 10}$$$$\oplus$$$$S_{1}^{\mathrm{new}}(\Gamma_1(40))$$$$^{\oplus 6}$$$$\oplus$$$$S_{1}^{\mathrm{new}}(\Gamma_1(76))$$$$^{\oplus 8}$$$$\oplus$$$$S_{1}^{\mathrm{new}}(\Gamma_1(80))$$$$^{\oplus 4}$$$$\oplus$$$$S_{1}^{\mathrm{new}}(\Gamma_1(95))$$$$^{\oplus 6}$$$$\oplus$$$$S_{1}^{\mathrm{new}}(\Gamma_1(152))$$$$^{\oplus 6}$$$$\oplus$$$$S_{1}^{\mathrm{new}}(\Gamma_1(160))$$$$^{\oplus 2}$$$$\oplus$$$$S_{1}^{\mathrm{new}}(\Gamma_1(190))$$$$^{\oplus 5}$$$$\oplus$$$$S_{1}^{\mathrm{new}}(\Gamma_1(304))$$$$^{\oplus 4}$$$$\oplus$$$$S_{1}^{\mathrm{new}}(\Gamma_1(380))$$$$^{\oplus 4}$$$$\oplus$$$$S_{1}^{\mathrm{new}}(\Gamma_1(608))$$$$^{\oplus 2}$$$$\oplus$$$$S_{1}^{\mathrm{new}}(\Gamma_1(760))$$$$^{\oplus 3}$$$$\oplus$$$$S_{1}^{\mathrm{new}}(\Gamma_1(1520))$$$$^{\oplus 2}$$$$\oplus$$$$S_{1}^{\mathrm{new}}(\Gamma_1(3040))$$$$^{\oplus 1}$$