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Properties

Label 8349.2
Level 8349
Weight 2
Dimension 1872048
Nonzero newspaces 104
Sturm bound 10222080

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Defining parameters

Level: \( N \) = \( 8349 = 3 \cdot 11^{2} \cdot 23 \)
Weight: \( k \) = \( 2 \)
Nonzero newspaces: \( 104 \)
Sturm bound: \(10222080\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_1(8349))\).

Total New Old
Modular forms 2569600 1883852 685748
Cusp forms 2541441 1872048 669393
Eisenstein series 28159 11804 16355

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_1(8349))\)

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
8349.2.a \(\chi_{8349}(1, \cdot)\) 8349.2.a.a 1 1
8349.2.a.b 1
8349.2.a.c 1
8349.2.a.d 1
8349.2.a.e 1
8349.2.a.f 2
8349.2.a.g 2
8349.2.a.h 2
8349.2.a.i 2
8349.2.a.j 2
8349.2.a.k 3
8349.2.a.l 3
8349.2.a.m 5
8349.2.a.n 6
8349.2.a.o 6
8349.2.a.p 6
8349.2.a.q 7
8349.2.a.r 7
8349.2.a.s 7
8349.2.a.t 7
8349.2.a.u 8
8349.2.a.v 8
8349.2.a.w 8
8349.2.a.x 10
8349.2.a.y 11
8349.2.a.z 11
8349.2.a.ba 12
8349.2.a.bb 12
8349.2.a.bc 12
8349.2.a.bd 12
8349.2.a.be 12
8349.2.a.bf 14
8349.2.a.bg 20
8349.2.a.bh 22
8349.2.a.bi 22
8349.2.a.bj 22
8349.2.a.bk 22
8349.2.a.bl 22
8349.2.a.bm 22
8349.2.a.bn 22
8349.2.a.bo 22
8349.2.b \(\chi_{8349}(2782, \cdot)\) n/a 432 1
8349.2.e \(\chi_{8349}(7382, \cdot)\) n/a 854 1
8349.2.f \(\chi_{8349}(6533, \cdot)\) n/a 792 1
8349.2.i \(\chi_{8349}(3106, \cdot)\) n/a 1584 4
8349.2.l \(\chi_{8349}(2048, \cdot)\) n/a 3168 4
8349.2.m \(\chi_{8349}(2138, \cdot)\) n/a 3392 4
8349.2.p \(\chi_{8349}(3748, \cdot)\) n/a 1728 4
8349.2.q \(\chi_{8349}(1189, \cdot)\) n/a 5280 10
8349.2.r \(\chi_{8349}(1090, \cdot)\) n/a 4360 10
8349.2.s \(\chi_{8349}(331, \cdot)\) n/a 5280 10
8349.2.t \(\chi_{8349}(760, \cdot)\) n/a 4840 10
8349.2.u \(\chi_{8349}(430, \cdot)\) n/a 5280 10
8349.2.v \(\chi_{8349}(463, \cdot)\) n/a 5280 10
8349.2.w \(\chi_{8349}(100, \cdot)\) n/a 5280 10
8349.2.x \(\chi_{8349}(397, \cdot)\) n/a 5280 10
8349.2.y \(\chi_{8349}(133, \cdot)\) n/a 5280 10
8349.2.z \(\chi_{8349}(232, \cdot)\) n/a 5280 10
8349.2.ba \(\chi_{8349}(265, \cdot)\) n/a 5280 10
8349.2.bb \(\chi_{8349}(1915, \cdot)\) n/a 5280 10
8349.2.bc \(\chi_{8349}(89, \cdot)\) n/a 10520 10
8349.2.bf \(\chi_{8349}(76, \cdot)\) n/a 5280 10
8349.2.bg \(\chi_{8349}(2375, \cdot)\) n/a 10520 10
8349.2.bt \(\chi_{8349}(98, \cdot)\) n/a 10520 10
8349.2.bv \(\chi_{8349}(593, \cdot)\) n/a 10520 10
8349.2.ce \(\chi_{8349}(692, \cdot)\) n/a 10520 10
8349.2.cf \(\chi_{8349}(131, \cdot)\) n/a 10520 10
8349.2.cg \(\chi_{8349}(461, \cdot)\) n/a 9680 10
8349.2.ch \(\chi_{8349}(725, \cdot)\) n/a 8480 10
8349.2.ci \(\chi_{8349}(164, \cdot)\) n/a 10520 10
8349.2.cj \(\chi_{8349}(32, \cdot)\) n/a 10520 10
8349.2.ck \(\chi_{8349}(1352, \cdot)\) n/a 10520 10
8349.2.cl \(\chi_{8349}(395, \cdot)\) n/a 10520 10
8349.2.cn \(\chi_{8349}(373, \cdot)\) n/a 5280 10
8349.2.cp \(\chi_{8349}(419, \cdot)\) n/a 10520 10
8349.2.cr \(\chi_{8349}(1376, \cdot)\) n/a 10520 10
8349.2.ct \(\chi_{8349}(914, \cdot)\) n/a 10520 10
8349.2.cu \(\chi_{8349}(56, \cdot)\) n/a 10520 10
8349.2.cv \(\chi_{8349}(551, \cdot)\) n/a 10520 10
8349.2.cw \(\chi_{8349}(617, \cdot)\) n/a 10520 10
8349.2.cx \(\chi_{8349}(122, \cdot)\) n/a 8540 10
8349.2.cy \(\chi_{8349}(1178, \cdot)\) n/a 10520 10
8349.2.cz \(\chi_{8349}(1739, \cdot)\) n/a 10520 10
8349.2.da \(\chi_{8349}(155, \cdot)\) n/a 10520 10
8349.2.dr \(\chi_{8349}(10, \cdot)\) n/a 5280 10
8349.2.ds \(\chi_{8349}(571, \cdot)\) n/a 5280 10
8349.2.dt \(\chi_{8349}(406, \cdot)\) n/a 5280 10
8349.2.du \(\chi_{8349}(43, \cdot)\) n/a 5280 10
8349.2.dv \(\chi_{8349}(241, \cdot)\) n/a 4320 10
8349.2.dw \(\chi_{8349}(505, \cdot)\) n/a 5280 10
8349.2.dx \(\chi_{8349}(274, \cdot)\) n/a 5280 10
8349.2.dy \(\chi_{8349}(1924, \cdot)\) n/a 5280 10
8349.2.ea \(\chi_{8349}(1792, \cdot)\) n/a 5280 10
8349.2.ec \(\chi_{8349}(175, \cdot)\) n/a 5280 10
8349.2.ee \(\chi_{8349}(815, \cdot)\) n/a 10520 10
8349.2.eh \(\chi_{8349}(791, \cdot)\) n/a 10520 10
8349.2.ei \(\chi_{8349}(262, \cdot)\) n/a 21120 40
8349.2.ej \(\chi_{8349}(223, \cdot)\) n/a 21120 40
8349.2.ek \(\chi_{8349}(190, \cdot)\) n/a 21120 40
8349.2.el \(\chi_{8349}(163, \cdot)\) n/a 21120 40
8349.2.em \(\chi_{8349}(196, \cdot)\) n/a 21120 40
8349.2.en \(\chi_{8349}(25, \cdot)\) n/a 21120 40
8349.2.eo \(\chi_{8349}(31, \cdot)\) n/a 21120 40
8349.2.ep \(\chi_{8349}(70, \cdot)\) n/a 19360 40
8349.2.eq \(\chi_{8349}(4, \cdot)\) n/a 21120 40
8349.2.er \(\chi_{8349}(124, \cdot)\) n/a 17280 40
8349.2.es \(\chi_{8349}(49, \cdot)\) n/a 21120 40
8349.2.et \(\chi_{8349}(58, \cdot)\) n/a 21120 40
8349.2.eu \(\chi_{8349}(41, \cdot)\) n/a 42080 40
8349.2.ex \(\chi_{8349}(212, \cdot)\) n/a 42080 40
8349.2.ez \(\chi_{8349}(79, \cdot)\) n/a 21120 40
8349.2.fb \(\chi_{8349}(178, \cdot)\) n/a 21120 40
8349.2.fc \(\chi_{8349}(442, \cdot)\) n/a 21120 40
8349.2.fd \(\chi_{8349}(160, \cdot)\) n/a 21120 40
8349.2.fe \(\chi_{8349}(40, \cdot)\) n/a 17280 40
8349.2.ff \(\chi_{8349}(7, \cdot)\) n/a 21120 40
8349.2.fg \(\chi_{8349}(337, \cdot)\) n/a 21120 40
8349.2.fh \(\chi_{8349}(19, \cdot)\) n/a 21120 40
8349.2.fi \(\chi_{8349}(106, \cdot)\) n/a 21120 40
8349.2.fr \(\chi_{8349}(310, \cdot)\) n/a 21120 40
8349.2.fu \(\chi_{8349}(20, \cdot)\) n/a 42080 40
8349.2.gd \(\chi_{8349}(158, \cdot)\) n/a 42080 40
8349.2.ge \(\chi_{8349}(14, \cdot)\) n/a 42080 40
8349.2.gf \(\chi_{8349}(53, \cdot)\) n/a 42080 40
8349.2.gg \(\chi_{8349}(245, \cdot)\) n/a 33920 40
8349.2.gh \(\chi_{8349}(203, \cdot)\) n/a 42080 40
8349.2.gi \(\chi_{8349}(137, \cdot)\) n/a 42080 40
8349.2.gj \(\chi_{8349}(113, \cdot)\) n/a 42080 40
8349.2.gk \(\chi_{8349}(5, \cdot)\) n/a 42080 40
8349.2.gm \(\chi_{8349}(86, \cdot)\) n/a 42080 40
8349.2.go \(\chi_{8349}(28, \cdot)\) n/a 21120 40
8349.2.gq \(\chi_{8349}(338, \cdot)\) n/a 42080 40
8349.2.gs \(\chi_{8349}(29, \cdot)\) n/a 42080 40
8349.2.gt \(\chi_{8349}(50, \cdot)\) n/a 42080 40
8349.2.gu \(\chi_{8349}(2, \cdot)\) n/a 42080 40
8349.2.gv \(\chi_{8349}(95, \cdot)\) n/a 42080 40
8349.2.gw \(\chi_{8349}(215, \cdot)\) n/a 33920 40
8349.2.gx \(\chi_{8349}(116, \cdot)\) n/a 38720 40
8349.2.gy \(\chi_{8349}(464, \cdot)\) n/a 42080 40
8349.2.gz \(\chi_{8349}(140, \cdot)\) n/a 42080 40
8349.2.hi \(\chi_{8349}(800, \cdot)\) n/a 42080 40
8349.2.hv \(\chi_{8349}(35, \cdot)\) n/a 42080 40
8349.2.hw \(\chi_{8349}(226, \cdot)\) n/a 21120 40
8349.2.hz \(\chi_{8349}(773, \cdot)\) n/a 42080 40

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

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_1(8349))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_1(8349)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_1(1))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(3))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(11))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(23))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(33))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(69))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(121))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(253))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(363))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(759))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(2783))\)\(^{\oplus 2}\)