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Properties

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

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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 available 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

\( S_{2}^{\mathrm{old}}(\Gamma_1(5265)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_1(1))\)\(^{\oplus 20}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(3))\)\(^{\oplus 16}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(5))\)\(^{\oplus 10}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(9))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(13))\)\(^{\oplus 10}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(15))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(27))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(39))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(45))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(65))\)\(^{\oplus 5}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(81))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(117))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(135))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(195))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(351))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(405))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(585))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(1053))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(1755))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(5265))\)\(^{\oplus 1}\)