# Properties

 Label 7360.2 Level 7360 Weight 2 Dimension 830412 Nonzero newspaces 56 Sturm bound 6488064

## Defining parameters

 Level: $$N$$ = $$7360 = 2^{6} \cdot 5 \cdot 23$$ Weight: $$k$$ = $$2$$ Nonzero newspaces: $$56$$ Sturm bound: $$6488064$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{2}(\Gamma_1(7360))$$.

Total New Old
Modular forms 1634688 835956 798732
Cusp forms 1609345 830412 778933
Eisenstein series 25343 5544 19799

## Decomposition of $$S_{2}^{\mathrm{new}}(\Gamma_1(7360))$$

We only show spaces with even 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
7360.2.a $$\chi_{7360}(1, \cdot)$$ 7360.2.a.a 1 1
7360.2.a.b 1
7360.2.a.c 1
7360.2.a.d 1
7360.2.a.e 1
7360.2.a.f 1
7360.2.a.g 1
7360.2.a.h 1
7360.2.a.i 1
7360.2.a.j 1
7360.2.a.k 1
7360.2.a.l 1
7360.2.a.m 1
7360.2.a.n 1
7360.2.a.o 1
7360.2.a.p 1
7360.2.a.q 1
7360.2.a.r 1
7360.2.a.s 1
7360.2.a.t 1
7360.2.a.u 1
7360.2.a.v 1
7360.2.a.w 1
7360.2.a.x 1
7360.2.a.y 1
7360.2.a.z 1
7360.2.a.ba 1
7360.2.a.bb 1
7360.2.a.bc 2
7360.2.a.bd 2
7360.2.a.be 2
7360.2.a.bf 2
7360.2.a.bg 2
7360.2.a.bh 2
7360.2.a.bi 2
7360.2.a.bj 2
7360.2.a.bk 2
7360.2.a.bl 2
7360.2.a.bm 2
7360.2.a.bn 2
7360.2.a.bo 2
7360.2.a.bp 2
7360.2.a.bq 2
7360.2.a.br 2
7360.2.a.bs 2
7360.2.a.bt 2
7360.2.a.bu 2
7360.2.a.bv 2
7360.2.a.bw 3
7360.2.a.bx 3
7360.2.a.by 3
7360.2.a.bz 3
7360.2.a.ca 3
7360.2.a.cb 3
7360.2.a.cc 3
7360.2.a.cd 3
7360.2.a.ce 3
7360.2.a.cf 3
7360.2.a.cg 4
7360.2.a.ch 4
7360.2.a.ci 4
7360.2.a.cj 4
7360.2.a.ck 5
7360.2.a.cl 5
7360.2.a.cm 5
7360.2.a.cn 5
7360.2.a.co 5
7360.2.a.cp 5
7360.2.a.cq 5
7360.2.a.cr 5
7360.2.a.cs 5
7360.2.a.ct 5
7360.2.a.cu 6
7360.2.a.cv 6
7360.2.b $$\chi_{7360}(3679, \cdot)$$ n/a 288 1
7360.2.e $$\chi_{7360}(5889, \cdot)$$ n/a 264 1
7360.2.f $$\chi_{7360}(3681, \cdot)$$ n/a 176 1
7360.2.i $$\chi_{7360}(1471, \cdot)$$ n/a 192 1
7360.2.j $$\chi_{7360}(2209, \cdot)$$ n/a 264 1
7360.2.m $$\chi_{7360}(7359, \cdot)$$ n/a 284 1
7360.2.n $$\chi_{7360}(5151, \cdot)$$ n/a 192 1
7360.2.r $$\chi_{7360}(6577, \cdot)$$ n/a 568 2
7360.2.t $$\chi_{7360}(47, \cdot)$$ n/a 528 2
7360.2.u $$\chi_{7360}(3311, \cdot)$$ n/a 384 2
7360.2.x $$\chi_{7360}(1841, \cdot)$$ n/a 352 2
7360.2.y $$\chi_{7360}(1793, \cdot)$$ n/a 568 2
7360.2.ba $$\chi_{7360}(2623, \cdot)$$ n/a 528 2
7360.2.bd $$\chi_{7360}(1887, \cdot)$$ n/a 528 2
7360.2.bf $$\chi_{7360}(1057, \cdot)$$ n/a 576 2
7360.2.bg $$\chi_{7360}(369, \cdot)$$ n/a 528 2
7360.2.bj $$\chi_{7360}(1839, \cdot)$$ n/a 568 2
7360.2.bk $$\chi_{7360}(3727, \cdot)$$ n/a 528 2
7360.2.bm $$\chi_{7360}(2897, \cdot)$$ n/a 568 2
7360.2.bp $$\chi_{7360}(1703, \cdot)$$ None 0 4
7360.2.br $$\chi_{7360}(137, \cdot)$$ None 0 4
7360.2.bs $$\chi_{7360}(919, \cdot)$$ None 0 4
7360.2.bu $$\chi_{7360}(921, \cdot)$$ None 0 4
7360.2.bx $$\chi_{7360}(551, \cdot)$$ None 0 4
7360.2.bz $$\chi_{7360}(1289, \cdot)$$ None 0 4
7360.2.ca $$\chi_{7360}(967, \cdot)$$ None 0 4
7360.2.cc $$\chi_{7360}(873, \cdot)$$ None 0 4
7360.2.ce $$\chi_{7360}(961, \cdot)$$ n/a 1920 10
7360.2.cg $$\chi_{7360}(413, \cdot)$$ n/a 9184 8
7360.2.ci $$\chi_{7360}(1243, \cdot)$$ n/a 8448 8
7360.2.ck $$\chi_{7360}(461, \cdot)$$ n/a 5632 8
7360.2.cl $$\chi_{7360}(829, \cdot)$$ n/a 8448 8
7360.2.co $$\chi_{7360}(459, \cdot)$$ n/a 9184 8
7360.2.cp $$\chi_{7360}(91, \cdot)$$ n/a 6144 8
7360.2.cr $$\chi_{7360}(1333, \cdot)$$ n/a 9184 8
7360.2.ct $$\chi_{7360}(323, \cdot)$$ n/a 8448 8
7360.2.cx $$\chi_{7360}(1631, \cdot)$$ n/a 1920 10
7360.2.cy $$\chi_{7360}(319, \cdot)$$ n/a 2840 10
7360.2.db $$\chi_{7360}(289, \cdot)$$ n/a 2880 10
7360.2.dc $$\chi_{7360}(191, \cdot)$$ n/a 1920 10
7360.2.df $$\chi_{7360}(1761, \cdot)$$ n/a 1920 10
7360.2.dg $$\chi_{7360}(449, \cdot)$$ n/a 2840 10
7360.2.dj $$\chi_{7360}(159, \cdot)$$ n/a 2880 10
7360.2.dl $$\chi_{7360}(17, \cdot)$$ n/a 5680 20
7360.2.dn $$\chi_{7360}(303, \cdot)$$ n/a 5680 20
7360.2.dp $$\chi_{7360}(79, \cdot)$$ n/a 5680 20
7360.2.dq $$\chi_{7360}(49, \cdot)$$ n/a 5680 20
7360.2.ds $$\chi_{7360}(33, \cdot)$$ n/a 5760 20
7360.2.du $$\chi_{7360}(223, \cdot)$$ n/a 5760 20
7360.2.dx $$\chi_{7360}(127, \cdot)$$ n/a 5680 20
7360.2.dz $$\chi_{7360}(513, \cdot)$$ n/a 5680 20
7360.2.eb $$\chi_{7360}(81, \cdot)$$ n/a 3840 20
7360.2.ec $$\chi_{7360}(111, \cdot)$$ n/a 3840 20
7360.2.ee $$\chi_{7360}(463, \cdot)$$ n/a 5680 20
7360.2.eg $$\chi_{7360}(273, \cdot)$$ n/a 5680 20
7360.2.ej $$\chi_{7360}(57, \cdot)$$ None 0 40
7360.2.el $$\chi_{7360}(167, \cdot)$$ None 0 40
7360.2.en $$\chi_{7360}(9, \cdot)$$ None 0 40
7360.2.ep $$\chi_{7360}(471, \cdot)$$ None 0 40
7360.2.eq $$\chi_{7360}(41, \cdot)$$ None 0 40
7360.2.es $$\chi_{7360}(199, \cdot)$$ None 0 40
7360.2.eu $$\chi_{7360}(153, \cdot)$$ None 0 40
7360.2.ew $$\chi_{7360}(87, \cdot)$$ None 0 40
7360.2.ey $$\chi_{7360}(3, \cdot)$$ n/a 91840 80
7360.2.fa $$\chi_{7360}(53, \cdot)$$ n/a 91840 80
7360.2.fd $$\chi_{7360}(11, \cdot)$$ n/a 61440 80
7360.2.fe $$\chi_{7360}(19, \cdot)$$ n/a 91840 80
7360.2.fh $$\chi_{7360}(29, \cdot)$$ n/a 91840 80
7360.2.fi $$\chi_{7360}(101, \cdot)$$ n/a 61440 80
7360.2.fl $$\chi_{7360}(123, \cdot)$$ n/a 91840 80
7360.2.fn $$\chi_{7360}(37, \cdot)$$ n/a 91840 80

"n/a" means that newforms for that character have not been added to the database yet

## Decomposition of $$S_{2}^{\mathrm{old}}(\Gamma_1(7360))$$ into lower level spaces

$$S_{2}^{\mathrm{old}}(\Gamma_1(7360)) \cong$$ $$S_{2}^{\mathrm{new}}(\Gamma_1(16))$$$$^{\oplus 12}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(20))$$$$^{\oplus 10}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(23))$$$$^{\oplus 14}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(32))$$$$^{\oplus 8}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(40))$$$$^{\oplus 8}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(46))$$$$^{\oplus 12}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(64))$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(80))$$$$^{\oplus 6}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(92))$$$$^{\oplus 10}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(115))$$$$^{\oplus 7}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(160))$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(184))$$$$^{\oplus 8}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(230))$$$$^{\oplus 6}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(320))$$$$^{\oplus 2}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(368))$$$$^{\oplus 6}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(460))$$$$^{\oplus 5}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(736))$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(920))$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(1472))$$$$^{\oplus 2}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(1840))$$$$^{\oplus 3}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(3680))$$$$^{\oplus 2}$$