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Properties

Label 9464.2
Level 9464
Weight 2
Dimension 1447860
Nonzero newspaces 90
Sturm bound 10902528

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Defining parameters

Level: \( N \) = \( 9464 = 2^{3} \cdot 7 \cdot 13^{2} \)
Weight: \( k \) = \( 2 \)
Nonzero newspaces: \( 90 \)
Sturm bound: \(10902528\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_1(9464))\).

Total New Old
Modular forms 2742048 1456040 1286008
Cusp forms 2709217 1447860 1261357
Eisenstein series 32831 8180 24651

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_1(9464))\)

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
9464.2.a \(\chi_{9464}(1, \cdot)\) 9464.2.a.a 1 1
9464.2.a.b 1
9464.2.a.c 1
9464.2.a.d 1
9464.2.a.e 1
9464.2.a.f 1
9464.2.a.g 1
9464.2.a.h 1
9464.2.a.i 2
9464.2.a.j 2
9464.2.a.k 2
9464.2.a.l 2
9464.2.a.m 2
9464.2.a.n 2
9464.2.a.o 2
9464.2.a.p 2
9464.2.a.q 2
9464.2.a.r 2
9464.2.a.s 2
9464.2.a.t 3
9464.2.a.u 3
9464.2.a.v 4
9464.2.a.w 4
9464.2.a.x 4
9464.2.a.y 4
9464.2.a.z 4
9464.2.a.ba 4
9464.2.a.bb 4
9464.2.a.bc 4
9464.2.a.bd 6
9464.2.a.be 6
9464.2.a.bf 6
9464.2.a.bg 6
9464.2.a.bh 7
9464.2.a.bi 7
9464.2.a.bj 12
9464.2.a.bk 12
9464.2.a.bl 12
9464.2.a.bm 12
9464.2.a.bn 12
9464.2.a.bo 12
9464.2.a.bp 12
9464.2.a.bq 12
9464.2.a.br 15
9464.2.a.bs 15
9464.2.b \(\chi_{9464}(4731, \cdot)\) n/a 1212 1
9464.2.c \(\chi_{9464}(4733, \cdot)\) n/a 930 1
9464.2.h \(\chi_{9464}(4395, \cdot)\) n/a 1218 1
9464.2.i \(\chi_{9464}(5069, \cdot)\) n/a 924 1
9464.2.j \(\chi_{9464}(9127, \cdot)\) None 0 1
9464.2.k \(\chi_{9464}(337, \cdot)\) n/a 232 1
9464.2.p \(\chi_{9464}(9463, \cdot)\) None 0 1
9464.2.q \(\chi_{9464}(529, \cdot)\) n/a 616 2
9464.2.r \(\chi_{9464}(1353, \cdot)\) n/a 620 2
9464.2.s \(\chi_{9464}(4033, \cdot)\) n/a 460 2
9464.2.t \(\chi_{9464}(7289, \cdot)\) n/a 616 2
9464.2.v \(\chi_{9464}(239, \cdot)\) None 0 2
9464.2.w \(\chi_{9464}(4633, \cdot)\) n/a 616 2
9464.2.z \(\chi_{9464}(99, \cdot)\) n/a 1848 2
9464.2.ba \(\chi_{9464}(4493, \cdot)\) n/a 2424 2
9464.2.be \(\chi_{9464}(485, \cdot)\) n/a 2424 2
9464.2.bf \(\chi_{9464}(4371, \cdot)\) n/a 2424 2
9464.2.bg \(\chi_{9464}(2557, \cdot)\) n/a 2424 2
9464.2.bh \(\chi_{9464}(6107, \cdot)\) n/a 2424 2
9464.2.bm \(\chi_{9464}(3865, \cdot)\) n/a 464 2
9464.2.bn \(\chi_{9464}(3695, \cdot)\) None 0 2
9464.2.bo \(\chi_{9464}(4079, \cdot)\) None 0 2
9464.2.bp \(\chi_{9464}(5407, \cdot)\) None 0 2
9464.2.by \(\chi_{9464}(1689, \cdot)\) n/a 616 2
9464.2.bz \(\chi_{9464}(5071, \cdot)\) None 0 2
9464.2.ca \(\chi_{9464}(1543, \cdot)\) None 0 2
9464.2.cb \(\chi_{9464}(7121, \cdot)\) n/a 616 2
9464.2.cc \(\chi_{9464}(3527, \cdot)\) None 0 2
9464.2.ch \(\chi_{9464}(1205, \cdot)\) n/a 1848 2
9464.2.ci \(\chi_{9464}(699, \cdot)\) n/a 2424 2
9464.2.cj \(\chi_{9464}(6421, \cdot)\) n/a 2424 2
9464.2.ck \(\chi_{9464}(339, \cdot)\) n/a 2436 2
9464.2.cl \(\chi_{9464}(6275, \cdot)\) n/a 2424 2
9464.2.cm \(\chi_{9464}(2389, \cdot)\) n/a 2424 2
9464.2.cv \(\chi_{9464}(4203, \cdot)\) n/a 2424 2
9464.2.cw \(\chi_{9464}(653, \cdot)\) n/a 2424 2
9464.2.cx \(\chi_{9464}(6085, \cdot)\) n/a 2436 2
9464.2.cy \(\chi_{9464}(675, \cdot)\) n/a 2424 2
9464.2.cz \(\chi_{9464}(1037, \cdot)\) n/a 1848 2
9464.2.da \(\chi_{9464}(867, \cdot)\) n/a 2424 2
9464.2.df \(\chi_{9464}(1375, \cdot)\) None 0 2
9464.2.dg \(\chi_{9464}(361, \cdot)\) n/a 616 2
9464.2.dh \(\chi_{9464}(4247, \cdot)\) None 0 2
9464.2.dl \(\chi_{9464}(2385, \cdot)\) n/a 1232 4
9464.2.dm \(\chi_{9464}(695, \cdot)\) None 0 4
9464.2.dp \(\chi_{9464}(3131, \cdot)\) n/a 4848 4
9464.2.ds \(\chi_{9464}(5389, \cdot)\) n/a 4848 4
9464.2.dt \(\chi_{9464}(437, \cdot)\) n/a 4848 4
9464.2.du \(\chi_{9464}(995, \cdot)\) n/a 3696 4
9464.2.dv \(\chi_{9464}(1451, \cdot)\) n/a 4848 4
9464.2.dy \(\chi_{9464}(1333, \cdot)\) n/a 4848 4
9464.2.eb \(\chi_{9464}(319, \cdot)\) None 0 4
9464.2.ee \(\chi_{9464}(657, \cdot)\) n/a 1232 4
9464.2.ef \(\chi_{9464}(577, \cdot)\) n/a 1232 4
9464.2.eg \(\chi_{9464}(5727, \cdot)\) None 0 4
9464.2.eh \(\chi_{9464}(1591, \cdot)\) None 0 4
9464.2.ek \(\chi_{9464}(89, \cdot)\) n/a 1232 4
9464.2.en \(\chi_{9464}(2117, \cdot)\) n/a 4848 4
9464.2.eo \(\chi_{9464}(2347, \cdot)\) n/a 4848 4
9464.2.eq \(\chi_{9464}(729, \cdot)\) n/a 3288 12
9464.2.er \(\chi_{9464}(727, \cdot)\) None 0 12
9464.2.ew \(\chi_{9464}(1065, \cdot)\) n/a 3264 12
9464.2.ex \(\chi_{9464}(391, \cdot)\) None 0 12
9464.2.ey \(\chi_{9464}(701, \cdot)\) n/a 13104 12
9464.2.ez \(\chi_{9464}(27, \cdot)\) n/a 17424 12
9464.2.fe \(\chi_{9464}(365, \cdot)\) n/a 13104 12
9464.2.ff \(\chi_{9464}(363, \cdot)\) n/a 17424 12
9464.2.fg \(\chi_{9464}(9, \cdot)\) n/a 8736 24
9464.2.fh \(\chi_{9464}(113, \cdot)\) n/a 6576 24
9464.2.fi \(\chi_{9464}(417, \cdot)\) n/a 8736 24
9464.2.fj \(\chi_{9464}(289, \cdot)\) n/a 8736 24
9464.2.fk \(\chi_{9464}(125, \cdot)\) n/a 34848 24
9464.2.fn \(\chi_{9464}(603, \cdot)\) n/a 26208 24
9464.2.fo \(\chi_{9464}(265, \cdot)\) n/a 8736 24
9464.2.fr \(\chi_{9464}(463, \cdot)\) None 0 24
9464.2.fu \(\chi_{9464}(367, \cdot)\) None 0 24
9464.2.fv \(\chi_{9464}(121, \cdot)\) n/a 8736 24
9464.2.fw \(\chi_{9464}(647, \cdot)\) None 0 24
9464.2.gb \(\chi_{9464}(139, \cdot)\) n/a 34848 24
9464.2.gc \(\chi_{9464}(309, \cdot)\) n/a 26208 24
9464.2.gd \(\chi_{9464}(467, \cdot)\) n/a 34848 24
9464.2.ge \(\chi_{9464}(53, \cdot)\) n/a 34848 24
9464.2.gf \(\chi_{9464}(165, \cdot)\) n/a 34848 24
9464.2.gg \(\chi_{9464}(75, \cdot)\) n/a 34848 24
9464.2.gp \(\chi_{9464}(205, \cdot)\) n/a 34848 24
9464.2.gq \(\chi_{9464}(451, \cdot)\) n/a 34848 24
9464.2.gr \(\chi_{9464}(131, \cdot)\) n/a 34848 24
9464.2.gs \(\chi_{9464}(389, \cdot)\) n/a 34848 24
9464.2.gt \(\chi_{9464}(251, \cdot)\) n/a 34848 24
9464.2.gu \(\chi_{9464}(29, \cdot)\) n/a 26208 24
9464.2.gz \(\chi_{9464}(335, \cdot)\) None 0 24
9464.2.ha \(\chi_{9464}(569, \cdot)\) n/a 8736 24
9464.2.hb \(\chi_{9464}(87, \cdot)\) None 0 24
9464.2.hc \(\chi_{9464}(495, \cdot)\) None 0 24
9464.2.hd \(\chi_{9464}(25, \cdot)\) n/a 8736 24
9464.2.hm \(\chi_{9464}(103, \cdot)\) None 0 24
9464.2.hn \(\chi_{9464}(199, \cdot)\) None 0 24
9464.2.ho \(\chi_{9464}(55, \cdot)\) None 0 24
9464.2.hp \(\chi_{9464}(225, \cdot)\) n/a 6528 24
9464.2.hu \(\chi_{9464}(283, \cdot)\) n/a 34848 24
9464.2.hv \(\chi_{9464}(373, \cdot)\) n/a 34848 24
9464.2.hw \(\chi_{9464}(3, \cdot)\) n/a 34848 24
9464.2.hx \(\chi_{9464}(725, \cdot)\) n/a 34848 24
9464.2.ia \(\chi_{9464}(11, \cdot)\) n/a 69696 48
9464.2.id \(\chi_{9464}(397, \cdot)\) n/a 69696 48
9464.2.ie \(\chi_{9464}(145, \cdot)\) n/a 17472 48
9464.2.ig \(\chi_{9464}(135, \cdot)\) None 0 48
9464.2.ih \(\chi_{9464}(15, \cdot)\) None 0 48
9464.2.im \(\chi_{9464}(73, \cdot)\) n/a 17472 48
9464.2.in \(\chi_{9464}(41, \cdot)\) n/a 17472 48
9464.2.ip \(\chi_{9464}(487, \cdot)\) None 0 48
9464.2.iq \(\chi_{9464}(45, \cdot)\) n/a 69696 48
9464.2.is \(\chi_{9464}(291, \cdot)\) n/a 69696 48
9464.2.it \(\chi_{9464}(267, \cdot)\) n/a 52416 48
9464.2.iy \(\chi_{9464}(5, \cdot)\) n/a 69696 48
9464.2.iz \(\chi_{9464}(293, \cdot)\) n/a 69696 48
9464.2.jb \(\chi_{9464}(123, \cdot)\) n/a 69696 48
9464.2.jc \(\chi_{9464}(375, \cdot)\) None 0 48
9464.2.jf \(\chi_{9464}(33, \cdot)\) n/a 17472 48

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

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_1(9464))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_1(9464)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_1(13))\)\(^{\oplus 16}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(14))\)\(^{\oplus 9}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(26))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(28))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(52))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(56))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(91))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(104))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(169))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(182))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(338))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(364))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(676))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(728))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(1183))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(1352))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(2366))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(4732))\)\(^{\oplus 2}\)