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Properties

Label 7644.2
Level 7644
Weight 2
Dimension 653526
Nonzero newspaces 120
Sturm bound 6322176

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Defining parameters

Level: \( N \) = \( 7644 = 2^{2} \cdot 3 \cdot 7^{2} \cdot 13 \)
Weight: \( k \) = \( 2 \)
Nonzero newspaces: \( 120 \)
Sturm bound: \(6322176\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_1(7644))\).

Total New Old
Modular forms 1594944 657790 937154
Cusp forms 1566145 653526 912619
Eisenstein series 28799 4264 24535

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_1(7644))\)

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
7644.2.a \(\chi_{7644}(1, \cdot)\) 7644.2.a.a 1 1
7644.2.a.b 1
7644.2.a.c 1
7644.2.a.d 1
7644.2.a.e 1
7644.2.a.f 1
7644.2.a.g 1
7644.2.a.h 1
7644.2.a.i 1
7644.2.a.j 1
7644.2.a.k 1
7644.2.a.l 2
7644.2.a.m 2
7644.2.a.n 2
7644.2.a.o 2
7644.2.a.p 2
7644.2.a.q 2
7644.2.a.r 2
7644.2.a.s 2
7644.2.a.t 3
7644.2.a.u 3
7644.2.a.v 3
7644.2.a.w 3
7644.2.a.x 3
7644.2.a.y 3
7644.2.a.z 3
7644.2.a.ba 5
7644.2.a.bb 5
7644.2.a.bc 6
7644.2.a.bd 6
7644.2.a.be 6
7644.2.a.bf 6
7644.2.c \(\chi_{7644}(391, \cdot)\) n/a 480 1
7644.2.e \(\chi_{7644}(4705, \cdot)\) 7644.2.e.a 2 1
7644.2.e.b 2
7644.2.e.c 2
7644.2.e.d 2
7644.2.e.e 2
7644.2.e.f 2
7644.2.e.g 2
7644.2.e.h 2
7644.2.e.i 4
7644.2.e.j 6
7644.2.e.k 6
7644.2.e.l 6
7644.2.e.m 6
7644.2.e.n 10
7644.2.e.o 10
7644.2.e.p 16
7644.2.e.q 16
7644.2.f \(\chi_{7644}(6371, \cdot)\) n/a 984 1
7644.2.h \(\chi_{7644}(3821, \cdot)\) n/a 188 1
7644.2.j \(\chi_{7644}(3431, \cdot)\) n/a 1128 1
7644.2.l \(\chi_{7644}(6761, \cdot)\) n/a 160 1
7644.2.o \(\chi_{7644}(5095, \cdot)\) n/a 560 1
7644.2.q \(\chi_{7644}(3901, \cdot)\) n/a 160 2
7644.2.r \(\chi_{7644}(2713, \cdot)\) n/a 186 2
7644.2.s \(\chi_{7644}(373, \cdot)\) n/a 186 2
7644.2.t \(\chi_{7644}(2941, \cdot)\) n/a 190 2
7644.2.u \(\chi_{7644}(1175, \cdot)\) n/a 2208 2
7644.2.x \(\chi_{7644}(2059, \cdot)\) n/a 1148 2
7644.2.z \(\chi_{7644}(2449, \cdot)\) n/a 184 2
7644.2.ba \(\chi_{7644}(785, \cdot)\) n/a 384 2
7644.2.bd \(\chi_{7644}(881, \cdot)\) n/a 372 2
7644.2.bf \(\chi_{7644}(1667, \cdot)\) n/a 2256 2
7644.2.bg \(\chi_{7644}(589, \cdot)\) n/a 194 2
7644.2.bi \(\chi_{7644}(3331, \cdot)\) n/a 1120 2
7644.2.bl \(\chi_{7644}(3461, \cdot)\) n/a 374 2
7644.2.bn \(\chi_{7644}(3215, \cdot)\) n/a 2208 2
7644.2.bo \(\chi_{7644}(2383, \cdot)\) n/a 1120 2
7644.2.bs \(\chi_{7644}(1195, \cdot)\) n/a 1120 2
7644.2.bv \(\chi_{7644}(4391, \cdot)\) n/a 2208 2
7644.2.bw \(\chi_{7644}(521, \cdot)\) n/a 320 2
7644.2.by \(\chi_{7644}(2027, \cdot)\) n/a 2208 2
7644.2.cb \(\chi_{7644}(4637, \cdot)\) n/a 374 2
7644.2.cd \(\chi_{7644}(3559, \cdot)\) n/a 1120 2
7644.2.cf \(\chi_{7644}(361, \cdot)\) n/a 186 2
7644.2.ch \(\chi_{7644}(607, \cdot)\) n/a 1120 2
7644.2.ck \(\chi_{7644}(1439, \cdot)\) n/a 2208 2
7644.2.cl \(\chi_{7644}(5225, \cdot)\) n/a 372 2
7644.2.cn \(\chi_{7644}(2627, \cdot)\) n/a 1920 2
7644.2.cq \(\chi_{7644}(1109, \cdot)\) n/a 374 2
7644.2.cr \(\chi_{7644}(5911, \cdot)\) n/a 1120 2
7644.2.cu \(\chi_{7644}(961, \cdot)\) n/a 188 2
7644.2.cw \(\chi_{7644}(1795, \cdot)\) n/a 960 2
7644.2.cx \(\chi_{7644}(5665, \cdot)\) n/a 186 2
7644.2.da \(\chi_{7644}(2285, \cdot)\) n/a 374 2
7644.2.dc \(\chi_{7644}(263, \cdot)\) n/a 2208 2
7644.2.de \(\chi_{7644}(979, \cdot)\) n/a 1120 2
7644.2.dh \(\chi_{7644}(2057, \cdot)\) n/a 372 2
7644.2.dj \(\chi_{7644}(491, \cdot)\) n/a 2256 2
7644.2.dk \(\chi_{7644}(1093, \cdot)\) n/a 672 6
7644.2.dm \(\chi_{7644}(227, \cdot)\) n/a 4416 4
7644.2.dn \(\chi_{7644}(3595, \cdot)\) n/a 2240 4
7644.2.dq \(\chi_{7644}(197, \cdot)\) n/a 764 4
7644.2.dr \(\chi_{7644}(4685, \cdot)\) n/a 744 4
7644.2.dt \(\chi_{7644}(557, \cdot)\) n/a 748 4
7644.2.dv \(\chi_{7644}(97, \cdot)\) n/a 376 4
7644.2.dy \(\chi_{7644}(1489, \cdot)\) n/a 372 4
7644.2.ea \(\chi_{7644}(3853, \cdot)\) n/a 376 4
7644.2.eb \(\chi_{7644}(1471, \cdot)\) n/a 2296 4
7644.2.ee \(\chi_{7644}(67, \cdot)\) n/a 2240 4
7644.2.eg \(\chi_{7644}(655, \cdot)\) n/a 2240 4
7644.2.ei \(\chi_{7644}(587, \cdot)\) n/a 4416 4
7644.2.ej \(\chi_{7644}(2579, \cdot)\) n/a 4416 4
7644.2.el \(\chi_{7644}(215, \cdot)\) n/a 4416 4
7644.2.en \(\chi_{7644}(1501, \cdot)\) n/a 372 4
7644.2.eq \(\chi_{7644}(2321, \cdot)\) n/a 748 4
7644.2.es \(\chi_{7644}(727, \cdot)\) n/a 4704 6
7644.2.ev \(\chi_{7644}(209, \cdot)\) n/a 1344 6
7644.2.ex \(\chi_{7644}(155, \cdot)\) n/a 9360 6
7644.2.ez \(\chi_{7644}(545, \cdot)\) n/a 1560 6
7644.2.fb \(\chi_{7644}(911, \cdot)\) n/a 8064 6
7644.2.fc \(\chi_{7644}(337, \cdot)\) n/a 792 6
7644.2.fe \(\chi_{7644}(1483, \cdot)\) n/a 4032 6
7644.2.fg \(\chi_{7644}(757, \cdot)\) n/a 1560 12
7644.2.fh \(\chi_{7644}(445, \cdot)\) n/a 1572 12
7644.2.fi \(\chi_{7644}(289, \cdot)\) n/a 1572 12
7644.2.fj \(\chi_{7644}(625, \cdot)\) n/a 1344 12
7644.2.fl \(\chi_{7644}(281, \cdot)\) n/a 3120 12
7644.2.fm \(\chi_{7644}(265, \cdot)\) n/a 1584 12
7644.2.fo \(\chi_{7644}(463, \cdot)\) n/a 9408 12
7644.2.fr \(\chi_{7644}(83, \cdot)\) n/a 18720 12
7644.2.fs \(\chi_{7644}(407, \cdot)\) n/a 18720 12
7644.2.fu \(\chi_{7644}(965, \cdot)\) n/a 3144 12
7644.2.fx \(\chi_{7644}(1063, \cdot)\) n/a 9408 12
7644.2.fz \(\chi_{7644}(191, \cdot)\) n/a 18720 12
7644.2.gb \(\chi_{7644}(101, \cdot)\) n/a 3132 12
7644.2.ge \(\chi_{7644}(205, \cdot)\) n/a 1572 12
7644.2.gf \(\chi_{7644}(703, \cdot)\) n/a 8064 12
7644.2.gh \(\chi_{7644}(25, \cdot)\) n/a 1560 12
7644.2.gk \(\chi_{7644}(451, \cdot)\) n/a 9408 12
7644.2.gl \(\chi_{7644}(17, \cdot)\) n/a 3132 12
7644.2.go \(\chi_{7644}(443, \cdot)\) n/a 16128 12
7644.2.gq \(\chi_{7644}(857, \cdot)\) n/a 3144 12
7644.2.gr \(\chi_{7644}(107, \cdot)\) n/a 18720 12
7644.2.gu \(\chi_{7644}(367, \cdot)\) n/a 9408 12
7644.2.gw \(\chi_{7644}(121, \cdot)\) n/a 1572 12
7644.2.gy \(\chi_{7644}(283, \cdot)\) n/a 9408 12
7644.2.ha \(\chi_{7644}(269, \cdot)\) n/a 3132 12
7644.2.hd \(\chi_{7644}(779, \cdot)\) n/a 18720 12
7644.2.hf \(\chi_{7644}(677, \cdot)\) n/a 2688 12
7644.2.hg \(\chi_{7644}(23, \cdot)\) n/a 18720 12
7644.2.hj \(\chi_{7644}(103, \cdot)\) n/a 9408 12
7644.2.hn \(\chi_{7644}(199, \cdot)\) n/a 9408 12
7644.2.ho \(\chi_{7644}(179, \cdot)\) n/a 18720 12
7644.2.hq \(\chi_{7644}(185, \cdot)\) n/a 3132 12
7644.2.ht \(\chi_{7644}(55, \cdot)\) n/a 9408 12
7644.2.hv \(\chi_{7644}(673, \cdot)\) n/a 1560 12
7644.2.hw \(\chi_{7644}(575, \cdot)\) n/a 18720 12
7644.2.hy \(\chi_{7644}(797, \cdot)\) n/a 3144 12
7644.2.ia \(\chi_{7644}(137, \cdot)\) n/a 6264 24
7644.2.id \(\chi_{7644}(145, \cdot)\) n/a 3144 24
7644.2.if \(\chi_{7644}(383, \cdot)\) n/a 37440 24
7644.2.ih \(\chi_{7644}(47, \cdot)\) n/a 37440 24
7644.2.ii \(\chi_{7644}(167, \cdot)\) n/a 37440 24
7644.2.ik \(\chi_{7644}(151, \cdot)\) n/a 18816 24
7644.2.im \(\chi_{7644}(163, \cdot)\) n/a 18816 24
7644.2.ip \(\chi_{7644}(379, \cdot)\) n/a 18816 24
7644.2.iq \(\chi_{7644}(73, \cdot)\) n/a 3120 24
7644.2.is \(\chi_{7644}(397, \cdot)\) n/a 3144 24
7644.2.iv \(\chi_{7644}(349, \cdot)\) n/a 3120 24
7644.2.ix \(\chi_{7644}(149, \cdot)\) n/a 6264 24
7644.2.iz \(\chi_{7644}(317, \cdot)\) n/a 6288 24
7644.2.ja \(\chi_{7644}(449, \cdot)\) n/a 6288 24
7644.2.jd \(\chi_{7644}(319, \cdot)\) n/a 18816 24
7644.2.je \(\chi_{7644}(59, \cdot)\) n/a 37440 24

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

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_1(7644))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_1(7644)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_1(13))\)\(^{\oplus 18}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(14))\)\(^{\oplus 16}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(21))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(26))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(28))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(39))\)\(^{\oplus 9}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(42))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(49))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(52))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(78))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(84))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(91))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(98))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(147))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(156))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(182))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(196))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(273))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(294))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(364))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(546))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(588))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(637))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(1092))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(1274))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(1911))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(2548))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(3822))\)\(^{\oplus 2}\)