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Properties

Label 5096.2
Level 5096
Weight 2
Dimension 419361
Nonzero newspaces 90
Sturm bound 3161088

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Defining parameters

Level: \( N \) = \( 5096 = 2^{3} \cdot 7^{2} \cdot 13 \)
Weight: \( k \) = \( 2 \)
Nonzero newspaces: \( 90 \)
Sturm bound: \(3161088\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_1(5096))\).

Total New Old
Modular forms 798912 423629 375283
Cusp forms 781633 419361 362272
Eisenstein series 17279 4268 13011

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_1(5096))\)

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
5096.2.a \(\chi_{5096}(1, \cdot)\) 5096.2.a.a 1 1
5096.2.a.b 1
5096.2.a.c 1
5096.2.a.d 1
5096.2.a.e 1
5096.2.a.f 1
5096.2.a.g 1
5096.2.a.h 1
5096.2.a.i 1
5096.2.a.j 1
5096.2.a.k 1
5096.2.a.l 2
5096.2.a.m 2
5096.2.a.n 2
5096.2.a.o 2
5096.2.a.p 2
5096.2.a.q 2
5096.2.a.r 4
5096.2.a.s 4
5096.2.a.t 4
5096.2.a.u 4
5096.2.a.v 4
5096.2.a.w 4
5096.2.a.x 5
5096.2.a.y 5
5096.2.a.z 7
5096.2.a.ba 7
5096.2.a.bb 8
5096.2.a.bc 8
5096.2.a.bd 8
5096.2.a.be 8
5096.2.a.bf 10
5096.2.a.bg 10
5096.2.b \(\chi_{5096}(2547, \cdot)\) n/a 552 1
5096.2.c \(\chi_{5096}(2549, \cdot)\) n/a 492 1
5096.2.h \(\chi_{5096}(2939, \cdot)\) n/a 480 1
5096.2.i \(\chi_{5096}(2157, \cdot)\) n/a 564 1
5096.2.j \(\chi_{5096}(391, \cdot)\) None 0 1
5096.2.k \(\chi_{5096}(4705, \cdot)\) n/a 144 1
5096.2.p \(\chi_{5096}(5095, \cdot)\) None 0 1
5096.2.q \(\chi_{5096}(1745, \cdot)\) n/a 280 2
5096.2.r \(\chi_{5096}(1145, \cdot)\) n/a 240 2
5096.2.s \(\chi_{5096}(393, \cdot)\) n/a 286 2
5096.2.t \(\chi_{5096}(1537, \cdot)\) n/a 280 2
5096.2.v \(\chi_{5096}(2647, \cdot)\) None 0 2
5096.2.w \(\chi_{5096}(489, \cdot)\) n/a 280 2
5096.2.z \(\chi_{5096}(99, \cdot)\) n/a 1128 2
5096.2.ba \(\chi_{5096}(3037, \cdot)\) n/a 1104 2
5096.2.be \(\chi_{5096}(1941, \cdot)\) n/a 1104 2
5096.2.bf \(\chi_{5096}(2187, \cdot)\) n/a 1104 2
5096.2.bg \(\chi_{5096}(373, \cdot)\) n/a 1104 2
5096.2.bh \(\chi_{5096}(1011, \cdot)\) n/a 1104 2
5096.2.bm \(\chi_{5096}(3137, \cdot)\) n/a 288 2
5096.2.bn \(\chi_{5096}(783, \cdot)\) None 0 2
5096.2.bo \(\chi_{5096}(2383, \cdot)\) None 0 2
5096.2.bp \(\chi_{5096}(3743, \cdot)\) None 0 2
5096.2.by \(\chi_{5096}(753, \cdot)\) n/a 280 2
5096.2.bz \(\chi_{5096}(4135, \cdot)\) None 0 2
5096.2.ca \(\chi_{5096}(815, \cdot)\) None 0 2
5096.2.cb \(\chi_{5096}(569, \cdot)\) n/a 280 2
5096.2.cc \(\chi_{5096}(3527, \cdot)\) None 0 2
5096.2.ch \(\chi_{5096}(2941, \cdot)\) n/a 1128 2
5096.2.ci \(\chi_{5096}(979, \cdot)\) n/a 1104 2
5096.2.cj \(\chi_{5096}(3301, \cdot)\) n/a 1104 2
5096.2.ck \(\chi_{5096}(1587, \cdot)\) n/a 960 2
5096.2.cl \(\chi_{5096}(1979, \cdot)\) n/a 1104 2
5096.2.cm \(\chi_{5096}(1733, \cdot)\) n/a 1104 2
5096.2.cv \(\chi_{5096}(803, \cdot)\) n/a 1104 2
5096.2.cw \(\chi_{5096}(165, \cdot)\) n/a 1104 2
5096.2.cx \(\chi_{5096}(3693, \cdot)\) n/a 960 2
5096.2.cy \(\chi_{5096}(1195, \cdot)\) n/a 1104 2
5096.2.cz \(\chi_{5096}(589, \cdot)\) n/a 1128 2
5096.2.da \(\chi_{5096}(3331, \cdot)\) n/a 1104 2
5096.2.df \(\chi_{5096}(2175, \cdot)\) None 0 2
5096.2.dg \(\chi_{5096}(361, \cdot)\) n/a 280 2
5096.2.dh \(\chi_{5096}(607, \cdot)\) None 0 2
5096.2.dk \(\chi_{5096}(729, \cdot)\) n/a 1008 6
5096.2.dm \(\chi_{5096}(1489, \cdot)\) n/a 560 4
5096.2.dn \(\chi_{5096}(1255, \cdot)\) None 0 4
5096.2.dq \(\chi_{5096}(275, \cdot)\) n/a 2208 4
5096.2.dt \(\chi_{5096}(293, \cdot)\) n/a 2208 4
5096.2.du \(\chi_{5096}(1685, \cdot)\) n/a 2208 4
5096.2.dv \(\chi_{5096}(2451, \cdot)\) n/a 2256 4
5096.2.dw \(\chi_{5096}(1243, \cdot)\) n/a 2208 4
5096.2.dz \(\chi_{5096}(509, \cdot)\) n/a 2208 4
5096.2.ec \(\chi_{5096}(1047, \cdot)\) None 0 4
5096.2.ef \(\chi_{5096}(97, \cdot)\) n/a 560 4
5096.2.eg \(\chi_{5096}(1097, \cdot)\) n/a 560 4
5096.2.eh \(\chi_{5096}(687, \cdot)\) None 0 4
5096.2.ei \(\chi_{5096}(655, \cdot)\) None 0 4
5096.2.el \(\chi_{5096}(1697, \cdot)\) n/a 560 4
5096.2.eo \(\chi_{5096}(717, \cdot)\) n/a 2208 4
5096.2.ep \(\chi_{5096}(67, \cdot)\) n/a 2208 4
5096.2.er \(\chi_{5096}(727, \cdot)\) None 0 6
5096.2.ew \(\chi_{5096}(337, \cdot)\) n/a 1176 6
5096.2.ex \(\chi_{5096}(1119, \cdot)\) None 0 6
5096.2.ey \(\chi_{5096}(701, \cdot)\) n/a 4680 6
5096.2.ez \(\chi_{5096}(27, \cdot)\) n/a 4032 6
5096.2.fe \(\chi_{5096}(365, \cdot)\) n/a 4032 6
5096.2.ff \(\chi_{5096}(363, \cdot)\) n/a 4680 6
5096.2.fg \(\chi_{5096}(9, \cdot)\) n/a 2352 12
5096.2.fh \(\chi_{5096}(113, \cdot)\) n/a 2352 12
5096.2.fi \(\chi_{5096}(417, \cdot)\) n/a 2016 12
5096.2.fj \(\chi_{5096}(289, \cdot)\) n/a 2352 12
5096.2.fl \(\chi_{5096}(125, \cdot)\) n/a 9360 12
5096.2.fm \(\chi_{5096}(603, \cdot)\) n/a 9360 12
5096.2.fp \(\chi_{5096}(265, \cdot)\) n/a 2352 12
5096.2.fq \(\chi_{5096}(239, \cdot)\) None 0 12
5096.2.fu \(\chi_{5096}(367, \cdot)\) None 0 12
5096.2.fv \(\chi_{5096}(121, \cdot)\) n/a 2352 12
5096.2.fw \(\chi_{5096}(647, \cdot)\) None 0 12
5096.2.gb \(\chi_{5096}(139, \cdot)\) n/a 9360 12
5096.2.gc \(\chi_{5096}(309, \cdot)\) n/a 9360 12
5096.2.gd \(\chi_{5096}(467, \cdot)\) n/a 9360 12
5096.2.ge \(\chi_{5096}(53, \cdot)\) n/a 8064 12
5096.2.gf \(\chi_{5096}(653, \cdot)\) n/a 9360 12
5096.2.gg \(\chi_{5096}(75, \cdot)\) n/a 9360 12
5096.2.gp \(\chi_{5096}(205, \cdot)\) n/a 9360 12
5096.2.gq \(\chi_{5096}(451, \cdot)\) n/a 9360 12
5096.2.gr \(\chi_{5096}(131, \cdot)\) n/a 8064 12
5096.2.gs \(\chi_{5096}(389, \cdot)\) n/a 9360 12
5096.2.gt \(\chi_{5096}(251, \cdot)\) n/a 9360 12
5096.2.gu \(\chi_{5096}(29, \cdot)\) n/a 9360 12
5096.2.gz \(\chi_{5096}(335, \cdot)\) None 0 12
5096.2.ha \(\chi_{5096}(641, \cdot)\) n/a 2352 12
5096.2.hb \(\chi_{5096}(87, \cdot)\) None 0 12
5096.2.hc \(\chi_{5096}(495, \cdot)\) None 0 12
5096.2.hd \(\chi_{5096}(25, \cdot)\) n/a 2352 12
5096.2.hm \(\chi_{5096}(103, \cdot)\) None 0 12
5096.2.hn \(\chi_{5096}(199, \cdot)\) None 0 12
5096.2.ho \(\chi_{5096}(55, \cdot)\) None 0 12
5096.2.hp \(\chi_{5096}(225, \cdot)\) n/a 2352 12
5096.2.hu \(\chi_{5096}(283, \cdot)\) n/a 9360 12
5096.2.hv \(\chi_{5096}(445, \cdot)\) n/a 9360 12
5096.2.hw \(\chi_{5096}(3, \cdot)\) n/a 9360 12
5096.2.hx \(\chi_{5096}(485, \cdot)\) n/a 9360 12
5096.2.ib \(\chi_{5096}(11, \cdot)\) n/a 18720 24
5096.2.ic \(\chi_{5096}(397, \cdot)\) n/a 18720 24
5096.2.if \(\chi_{5096}(89, \cdot)\) n/a 4704 24
5096.2.ii \(\chi_{5096}(135, \cdot)\) None 0 24
5096.2.ij \(\chi_{5096}(15, \cdot)\) None 0 24
5096.2.ik \(\chi_{5096}(73, \cdot)\) n/a 4704 24
5096.2.il \(\chi_{5096}(41, \cdot)\) n/a 4704 24
5096.2.io \(\chi_{5096}(319, \cdot)\) None 0 24
5096.2.ir \(\chi_{5096}(45, \cdot)\) n/a 18720 24
5096.2.iu \(\chi_{5096}(291, \cdot)\) n/a 18720 24
5096.2.iv \(\chi_{5096}(267, \cdot)\) n/a 18720 24
5096.2.iw \(\chi_{5096}(5, \cdot)\) n/a 18720 24
5096.2.ix \(\chi_{5096}(349, \cdot)\) n/a 18720 24
5096.2.ja \(\chi_{5096}(123, \cdot)\) n/a 18720 24
5096.2.jd \(\chi_{5096}(375, \cdot)\) None 0 24
5096.2.je \(\chi_{5096}(33, \cdot)\) n/a 4704 24

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

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_1(5096))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_1(5096)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_1(1))\)\(^{\oplus 24}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(2))\)\(^{\oplus 18}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(4))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(7))\)\(^{\oplus 16}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(8))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(13))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(14))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(26))\)\(^{\oplus 9}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(28))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(49))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(52))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(56))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(91))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(98))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(104))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(182))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(196))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(364))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(392))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(637))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(728))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(1274))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(2548))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(5096))\)\(^{\oplus 1}\)