# Properties

 Label 3520.1 Level 3520 Weight 1 Dimension 114 Nonzero newspaces 7 Newform subspaces 25 Sturm bound 737280 Trace bound 9

## Defining parameters

 Level: $$N$$ = $$3520 = 2^{6} \cdot 5 \cdot 11$$ Weight: $$k$$ = $$1$$ Nonzero newspaces: $$7$$ Newform subspaces: $$25$$ Sturm bound: $$737280$$ Trace bound: $$9$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{1}(\Gamma_1(3520))$$.

Total New Old
Modular forms 6212 1302 4910
Cusp forms 452 114 338
Eisenstein series 5760 1188 4572

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

$$D_n$$ $$A_4$$ $$S_4$$ $$A_5$$
Dimension 114 0 0 0

## Trace form

 $$114 q - 4 q^{5} + 6 q^{9} + O(q^{10})$$ $$114 q - 4 q^{5} + 6 q^{9} - 20 q^{41} + 10 q^{45} - 46 q^{49} + 12 q^{53} - 40 q^{59} - 4 q^{69} - 32 q^{71} - 34 q^{81} + 8 q^{89} + 8 q^{91} - 12 q^{93} + O(q^{100})$$

## Decomposition of $$S_{1}^{\mathrm{new}}(\Gamma_1(3520))$$

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
3520.1.d $$\chi_{3520}(1121, \cdot)$$ None 0 1
3520.1.e $$\chi_{3520}(2751, \cdot)$$ None 0 1
3520.1.h $$\chi_{3520}(2399, \cdot)$$ None 0 1
3520.1.i $$\chi_{3520}(769, \cdot)$$ 3520.1.i.a 1 1
3520.1.i.b 1
3520.1.i.c 2
3520.1.i.d 2
3520.1.i.e 4
3520.1.j $$\chi_{3520}(2881, \cdot)$$ None 0 1
3520.1.k $$\chi_{3520}(991, \cdot)$$ None 0 1
3520.1.n $$\chi_{3520}(639, \cdot)$$ None 0 1
3520.1.o $$\chi_{3520}(2529, \cdot)$$ 3520.1.o.a 2 1
3520.1.o.b 2
3520.1.o.c 4
3520.1.o.d 4
3520.1.q $$\chi_{3520}(2287, \cdot)$$ None 0 2
3520.1.r $$\chi_{3520}(177, \cdot)$$ None 0 2
3520.1.u $$\chi_{3520}(1519, \cdot)$$ None 0 2
3520.1.x $$\chi_{3520}(1649, \cdot)$$ 3520.1.x.a 8 2
3520.1.y $$\chi_{3520}(703, \cdot)$$ 3520.1.y.a 2 2
3520.1.y.b 2
3520.1.y.c 4
3520.1.y.d 4
3520.1.ba $$\chi_{3520}(2113, \cdot)$$ None 0 2
3520.1.bc $$\chi_{3520}(353, \cdot)$$ None 0 2
3520.1.be $$\chi_{3520}(2463, \cdot)$$ 3520.1.be.a 2 2
3520.1.be.b 2
3520.1.be.c 2
3520.1.be.d 2
3520.1.be.e 4
3520.1.be.f 4
3520.1.be.g 4
3520.1.be.h 4
3520.1.bg $$\chi_{3520}(241, \cdot)$$ None 0 2
3520.1.bj $$\chi_{3520}(111, \cdot)$$ None 0 2
3520.1.bm $$\chi_{3520}(527, \cdot)$$ None 0 2
3520.1.bn $$\chi_{3520}(1937, \cdot)$$ None 0 2
3520.1.bq $$\chi_{3520}(1497, \cdot)$$ None 0 4
3520.1.br $$\chi_{3520}(967, \cdot)$$ None 0 4
3520.1.bu $$\chi_{3520}(551, \cdot)$$ None 0 4
3520.1.bw $$\chi_{3520}(329, \cdot)$$ None 0 4
3520.1.bx $$\chi_{3520}(199, \cdot)$$ None 0 4
3520.1.bz $$\chi_{3520}(681, \cdot)$$ None 0 4
3520.1.cb $$\chi_{3520}(87, \cdot)$$ None 0 4
3520.1.ce $$\chi_{3520}(617, \cdot)$$ None 0 4
3520.1.cg $$\chi_{3520}(1249, \cdot)$$ 3520.1.cg.a 8 4
3520.1.cg.b 8
3520.1.ch $$\chi_{3520}(1279, \cdot)$$ None 0 4
3520.1.ck $$\chi_{3520}(31, \cdot)$$ None 0 4
3520.1.cl $$\chi_{3520}(321, \cdot)$$ None 0 4
3520.1.cm $$\chi_{3520}(129, \cdot)$$ None 0 4
3520.1.cn $$\chi_{3520}(159, \cdot)$$ None 0 4
3520.1.cq $$\chi_{3520}(191, \cdot)$$ None 0 4
3520.1.cr $$\chi_{3520}(161, \cdot)$$ None 0 4
3520.1.cu $$\chi_{3520}(133, \cdot)$$ None 0 8
3520.1.cw $$\chi_{3520}(483, \cdot)$$ None 0 8
3520.1.cy $$\chi_{3520}(21, \cdot)$$ None 0 8
3520.1.db $$\chi_{3520}(109, \cdot)$$ 3520.1.db.a 32 8
3520.1.dc $$\chi_{3520}(331, \cdot)$$ None 0 8
3520.1.df $$\chi_{3520}(419, \cdot)$$ None 0 8
3520.1.dh $$\chi_{3520}(573, \cdot)$$ None 0 8
3520.1.dj $$\chi_{3520}(43, \cdot)$$ None 0 8
3520.1.dk $$\chi_{3520}(113, \cdot)$$ None 0 8
3520.1.dl $$\chi_{3520}(303, \cdot)$$ None 0 8
3520.1.dp $$\chi_{3520}(751, \cdot)$$ None 0 8
3520.1.dq $$\chi_{3520}(721, \cdot)$$ None 0 8
3520.1.dt $$\chi_{3520}(97, \cdot)$$ None 0 8
3520.1.dv $$\chi_{3520}(607, \cdot)$$ None 0 8
3520.1.dx $$\chi_{3520}(63, \cdot)$$ None 0 8
3520.1.dz $$\chi_{3520}(257, \cdot)$$ None 0 8
3520.1.eb $$\chi_{3520}(369, \cdot)$$ None 0 8
3520.1.ec $$\chi_{3520}(399, \cdot)$$ None 0 8
3520.1.eg $$\chi_{3520}(273, \cdot)$$ None 0 8
3520.1.eh $$\chi_{3520}(783, \cdot)$$ None 0 8
3520.1.ej $$\chi_{3520}(567, \cdot)$$ None 0 16
3520.1.ek $$\chi_{3520}(137, \cdot)$$ None 0 16
3520.1.en $$\chi_{3520}(41, \cdot)$$ None 0 16
3520.1.ep $$\chi_{3520}(119, \cdot)$$ None 0 16
3520.1.eq $$\chi_{3520}(249, \cdot)$$ None 0 16
3520.1.es $$\chi_{3520}(71, \cdot)$$ None 0 16
3520.1.eu $$\chi_{3520}(377, \cdot)$$ None 0 16
3520.1.ex $$\chi_{3520}(7, \cdot)$$ None 0 16
3520.1.ey $$\chi_{3520}(123, \cdot)$$ None 0 32
3520.1.fa $$\chi_{3520}(37, \cdot)$$ None 0 32
3520.1.fc $$\chi_{3520}(59, \cdot)$$ None 0 32
3520.1.ff $$\chi_{3520}(91, \cdot)$$ None 0 32
3520.1.fg $$\chi_{3520}(29, \cdot)$$ None 0 32
3520.1.fj $$\chi_{3520}(61, \cdot)$$ None 0 32
3520.1.fl $$\chi_{3520}(83, \cdot)$$ None 0 32
3520.1.fn $$\chi_{3520}(53, \cdot)$$ None 0 32

## Decomposition of $$S_{1}^{\mathrm{old}}(\Gamma_1(3520))$$ into lower level spaces

$$S_{1}^{\mathrm{old}}(\Gamma_1(3520)) \cong$$ $$S_{1}^{\mathrm{new}}(\Gamma_1(44))$$$$^{\oplus 10}$$$$\oplus$$$$S_{1}^{\mathrm{new}}(\Gamma_1(55))$$$$^{\oplus 7}$$$$\oplus$$$$S_{1}^{\mathrm{new}}(\Gamma_1(80))$$$$^{\oplus 6}$$$$\oplus$$$$S_{1}^{\mathrm{new}}(\Gamma_1(88))$$$$^{\oplus 8}$$$$\oplus$$$$S_{1}^{\mathrm{new}}(\Gamma_1(160))$$$$^{\oplus 4}$$$$\oplus$$$$S_{1}^{\mathrm{new}}(\Gamma_1(176))$$$$^{\oplus 6}$$$$\oplus$$$$S_{1}^{\mathrm{new}}(\Gamma_1(220))$$$$^{\oplus 5}$$$$\oplus$$$$S_{1}^{\mathrm{new}}(\Gamma_1(320))$$$$^{\oplus 2}$$$$\oplus$$$$S_{1}^{\mathrm{new}}(\Gamma_1(352))$$$$^{\oplus 4}$$$$\oplus$$$$S_{1}^{\mathrm{new}}(\Gamma_1(440))$$$$^{\oplus 4}$$$$\oplus$$$$S_{1}^{\mathrm{new}}(\Gamma_1(704))$$$$^{\oplus 2}$$$$\oplus$$$$S_{1}^{\mathrm{new}}(\Gamma_1(880))$$$$^{\oplus 3}$$$$\oplus$$$$S_{1}^{\mathrm{new}}(\Gamma_1(1760))$$$$^{\oplus 2}$$