# Properties

 Label 5265.2 Level 5265 Weight 2 Dimension 697488 Nonzero newspaces 110 Sturm bound 3919104

## Defining parameters

 Level: $$N$$ = $$5265 = 3^{4} \cdot 5 \cdot 13$$ Weight: $$k$$ = $$2$$ Nonzero newspaces: $$110$$ Sturm bound: $$3919104$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{2}(\Gamma_1(5265))$$.

Total New Old
Modular forms 990144 704880 285264
Cusp forms 969409 697488 271921
Eisenstein series 20735 7392 13343

## Decomposition of $$S_{2}^{\mathrm{new}}(\Gamma_1(5265))$$

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
5265.2.a $$\chi_{5265}(1, \cdot)$$ 5265.2.a.a 1 1
5265.2.a.b 1
5265.2.a.c 1
5265.2.a.d 1
5265.2.a.e 1
5265.2.a.f 1
5265.2.a.g 1
5265.2.a.h 1
5265.2.a.i 1
5265.2.a.j 1
5265.2.a.k 1
5265.2.a.l 1
5265.2.a.m 1
5265.2.a.n 1
5265.2.a.o 1
5265.2.a.p 1
5265.2.a.q 2
5265.2.a.r 2
5265.2.a.s 3
5265.2.a.t 3
5265.2.a.u 4
5265.2.a.v 4
5265.2.a.w 6
5265.2.a.x 6
5265.2.a.y 7
5265.2.a.z 7
5265.2.a.ba 8
5265.2.a.bb 8
5265.2.a.bc 8
5265.2.a.bd 8
5265.2.a.be 8
5265.2.a.bf 8
5265.2.a.bg 13
5265.2.a.bh 13
5265.2.a.bi 14
5265.2.a.bj 14
5265.2.a.bk 15
5265.2.a.bl 15
5265.2.b $$\chi_{5265}(4861, \cdot)$$ n/a 224 1
5265.2.c $$\chi_{5265}(1054, \cdot)$$ n/a 288 1
5265.2.h $$\chi_{5265}(649, \cdot)$$ n/a 328 1
5265.2.i $$\chi_{5265}(1756, \cdot)$$ n/a 384 2
5265.2.j $$\chi_{5265}(406, \cdot)$$ n/a 448 2
5265.2.k $$\chi_{5265}(3376, \cdot)$$ n/a 448 2
5265.2.l $$\chi_{5265}(2161, \cdot)$$ n/a 448 2
5265.2.n $$\chi_{5265}(892, \cdot)$$ n/a 656 2
5265.2.p $$\chi_{5265}(1457, \cdot)$$ n/a 576 2
5265.2.q $$\chi_{5265}(1214, \cdot)$$ n/a 656 2
5265.2.r $$\chi_{5265}(161, \cdot)$$ n/a 448 2
5265.2.v $$\chi_{5265}(1052, \cdot)$$ n/a 656 2
5265.2.w $$\chi_{5265}(2917, \cdot)$$ n/a 656 2
5265.2.ba $$\chi_{5265}(946, \cdot)$$ n/a 448 2
5265.2.bb $$\chi_{5265}(919, \cdot)$$ n/a 664 2
5265.2.be $$\chi_{5265}(2404, \cdot)$$ n/a 664 2
5265.2.bf $$\chi_{5265}(244, \cdot)$$ n/a 656 2
5265.2.bk $$\chi_{5265}(784, \cdot)$$ n/a 664 2
5265.2.bl $$\chi_{5265}(4429, \cdot)$$ n/a 664 2
5265.2.bm $$\chi_{5265}(2701, \cdot)$$ n/a 448 2
5265.2.br $$\chi_{5265}(2809, \cdot)$$ n/a 576 2
5265.2.bs $$\chi_{5265}(1459, \cdot)$$ n/a 656 2
5265.2.bt $$\chi_{5265}(1351, \cdot)$$ n/a 448 2
5265.2.bu $$\chi_{5265}(3241, \cdot)$$ n/a 448 2
5265.2.bx $$\chi_{5265}(1999, \cdot)$$ n/a 664 2
5265.2.ca $$\chi_{5265}(586, \cdot)$$ n/a 864 6
5265.2.cb $$\chi_{5265}(451, \cdot)$$ n/a 1008 6
5265.2.cc $$\chi_{5265}(991, \cdot)$$ n/a 1008 6
5265.2.cd $$\chi_{5265}(622, \cdot)$$ n/a 1328 4
5265.2.cf $$\chi_{5265}(1918, \cdot)$$ n/a 1328 4
5265.2.ci $$\chi_{5265}(163, \cdot)$$ n/a 1312 4
5265.2.cj $$\chi_{5265}(1162, \cdot)$$ n/a 1328 4
5265.2.cl $$\chi_{5265}(107, \cdot)$$ n/a 1328 4
5265.2.cp $$\chi_{5265}(431, \cdot)$$ n/a 896 4
5265.2.cq $$\chi_{5265}(539, \cdot)$$ n/a 1328 4
5265.2.cr $$\chi_{5265}(998, \cdot)$$ n/a 1328 4
5265.2.cu $$\chi_{5265}(2402, \cdot)$$ n/a 1328 4
5265.2.cv $$\chi_{5265}(1403, \cdot)$$ n/a 1328 4
5265.2.cy $$\chi_{5265}(647, \cdot)$$ n/a 1312 4
5265.2.cz $$\chi_{5265}(566, \cdot)$$ n/a 896 4
5265.2.da $$\chi_{5265}(1619, \cdot)$$ n/a 1312 4
5265.2.df $$\chi_{5265}(944, \cdot)$$ n/a 1328 4
5265.2.dg $$\chi_{5265}(1241, \cdot)$$ n/a 896 4
5265.2.dh $$\chi_{5265}(2294, \cdot)$$ n/a 1328 4
5265.2.di $$\chi_{5265}(1646, \cdot)$$ n/a 896 4
5265.2.dm $$\chi_{5265}(53, \cdot)$$ n/a 1152 4
5265.2.dn $$\chi_{5265}(458, \cdot)$$ n/a 1328 4
5265.2.dq $$\chi_{5265}(1862, \cdot)$$ n/a 1312 4
5265.2.ds $$\chi_{5265}(1783, \cdot)$$ n/a 1312 4
5265.2.dt $$\chi_{5265}(1513, \cdot)$$ n/a 1328 4
5265.2.dw $$\chi_{5265}(28, \cdot)$$ n/a 1328 4
5265.2.dy $$\chi_{5265}(1432, \cdot)$$ n/a 1328 4
5265.2.dz $$\chi_{5265}(199, \cdot)$$ n/a 1488 6
5265.2.ed $$\chi_{5265}(1369, \cdot)$$ n/a 1488 6
5265.2.eg $$\chi_{5265}(64, \cdot)$$ n/a 1488 6
5265.2.ej $$\chi_{5265}(289, \cdot)$$ n/a 1488 6
5265.2.el $$\chi_{5265}(316, \cdot)$$ n/a 1008 6
5265.2.em $$\chi_{5265}(181, \cdot)$$ n/a 1008 6
5265.2.eo $$\chi_{5265}(469, \cdot)$$ n/a 1296 6
5265.2.er $$\chi_{5265}(874, \cdot)$$ n/a 1488 6
5265.2.et $$\chi_{5265}(901, \cdot)$$ n/a 1008 6
5265.2.eu $$\chi_{5265}(16, \cdot)$$ n/a 9072 18
5265.2.ev $$\chi_{5265}(196, \cdot)$$ n/a 7776 18
5265.2.ew $$\chi_{5265}(61, \cdot)$$ n/a 9072 18
5265.2.ex $$\chi_{5265}(73, \cdot)$$ n/a 2976 12
5265.2.fa $$\chi_{5265}(388, \cdot)$$ n/a 2976 12
5265.2.fb $$\chi_{5265}(262, \cdot)$$ n/a 2976 12
5265.2.fd $$\chi_{5265}(89, \cdot)$$ n/a 2976 12
5265.2.ff $$\chi_{5265}(476, \cdot)$$ n/a 2016 12
5265.2.fh $$\chi_{5265}(206, \cdot)$$ n/a 2016 12
5265.2.fj $$\chi_{5265}(692, \cdot)$$ n/a 2976 12
5265.2.fn $$\chi_{5265}(233, \cdot)$$ n/a 2976 12
5265.2.fo $$\chi_{5265}(17, \cdot)$$ n/a 2976 12
5265.2.fp $$\chi_{5265}(152, \cdot)$$ n/a 2976 12
5265.2.fq $$\chi_{5265}(287, \cdot)$$ n/a 2592 12
5265.2.fu $$\chi_{5265}(602, \cdot)$$ n/a 2976 12
5265.2.fw $$\chi_{5265}(314, \cdot)$$ n/a 2976 12
5265.2.fy $$\chi_{5265}(44, \cdot)$$ n/a 2976 12
5265.2.ga $$\chi_{5265}(71, \cdot)$$ n/a 2016 12
5265.2.gc $$\chi_{5265}(253, \cdot)$$ n/a 2976 12
5265.2.gd $$\chi_{5265}(37, \cdot)$$ n/a 2976 12
5265.2.gg $$\chi_{5265}(307, \cdot)$$ n/a 2976 12
5265.2.gh $$\chi_{5265}(166, \cdot)$$ n/a 9072 18
5265.2.gk $$\chi_{5265}(94, \cdot)$$ n/a 13536 18
5265.2.gn $$\chi_{5265}(259, \cdot)$$ n/a 13536 18
5265.2.gp $$\chi_{5265}(4, \cdot)$$ n/a 13536 18
5265.2.gs $$\chi_{5265}(121, \cdot)$$ n/a 9072 18
5265.2.gu $$\chi_{5265}(376, \cdot)$$ n/a 9072 18
5265.2.gv $$\chi_{5265}(79, \cdot)$$ n/a 11664 18
5265.2.gx $$\chi_{5265}(139, \cdot)$$ n/a 13536 18
5265.2.hb $$\chi_{5265}(49, \cdot)$$ n/a 13536 18
5265.2.hc $$\chi_{5265}(67, \cdot)$$ n/a 27072 36
5265.2.hf $$\chi_{5265}(112, \cdot)$$ n/a 27072 36
5265.2.hh $$\chi_{5265}(58, \cdot)$$ n/a 27072 36
5265.2.hj $$\chi_{5265}(254, \cdot)$$ n/a 27072 36
5265.2.hk $$\chi_{5265}(59, \cdot)$$ n/a 27072 36
5265.2.hn $$\chi_{5265}(164, \cdot)$$ n/a 27072 36
5265.2.hp $$\chi_{5265}(23, \cdot)$$ n/a 27072 36
5265.2.hq $$\chi_{5265}(38, \cdot)$$ n/a 27072 36
5265.2.ht $$\chi_{5265}(212, \cdot)$$ n/a 27072 36
5265.2.hv $$\chi_{5265}(92, \cdot)$$ n/a 23328 36
5265.2.hw $$\chi_{5265}(68, \cdot)$$ n/a 27072 36
5265.2.hz $$\chi_{5265}(113, \cdot)$$ n/a 27072 36
5265.2.ia $$\chi_{5265}(86, \cdot)$$ n/a 18144 36
5265.2.id $$\chi_{5265}(11, \cdot)$$ n/a 18144 36
5265.2.ie $$\chi_{5265}(41, \cdot)$$ n/a 18144 36
5265.2.ih $$\chi_{5265}(187, \cdot)$$ n/a 27072 36
5265.2.ij $$\chi_{5265}(292, \cdot)$$ n/a 27072 36
5265.2.ik $$\chi_{5265}(7, \cdot)$$ n/a 27072 36

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

## Decomposition of $$S_{2}^{\mathrm{old}}(\Gamma_1(5265))$$ into lower level spaces

$$S_{2}^{\mathrm{old}}(\Gamma_1(5265)) \cong$$ $$S_{2}^{\mathrm{new}}(\Gamma_1(13))$$$$^{\oplus 10}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(15))$$$$^{\oplus 8}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(27))$$$$^{\oplus 8}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(39))$$$$^{\oplus 8}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(45))$$$$^{\oplus 6}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(65))$$$$^{\oplus 5}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(81))$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(117))$$$$^{\oplus 6}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(135))$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(195))$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(351))$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(405))$$$$^{\oplus 2}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(585))$$$$^{\oplus 3}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(1053))$$$$^{\oplus 2}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(1755))$$$$^{\oplus 2}$$