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Properties

Label 7254.2
Level 7254
Weight 2
Dimension 377690
Nonzero newspaces 168
Sturm bound 5806080

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Defining parameters

Level: \( N \) = \( 7254 = 2 \cdot 3^{2} \cdot 13 \cdot 31 \)
Weight: \( k \) = \( 2 \)
Nonzero newspaces: \( 168 \)
Sturm bound: \(5806080\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_1(7254))\).

Total New Old
Modular forms 1463040 377690 1085350
Cusp forms 1440001 377690 1062311
Eisenstein series 23039 0 23039

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_1(7254))\)

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
7254.2.a \(\chi_{7254}(1, \cdot)\) 7254.2.a.a 1 1
7254.2.a.b 1
7254.2.a.c 1
7254.2.a.d 1
7254.2.a.e 1
7254.2.a.f 1
7254.2.a.g 1
7254.2.a.h 1
7254.2.a.i 1
7254.2.a.j 1
7254.2.a.k 1
7254.2.a.l 1
7254.2.a.m 1
7254.2.a.n 1
7254.2.a.o 1
7254.2.a.p 2
7254.2.a.q 2
7254.2.a.r 2
7254.2.a.s 2
7254.2.a.t 2
7254.2.a.u 2
7254.2.a.v 2
7254.2.a.w 2
7254.2.a.x 3
7254.2.a.y 3
7254.2.a.z 4
7254.2.a.ba 4
7254.2.a.bb 4
7254.2.a.bc 4
7254.2.a.bd 5
7254.2.a.be 5
7254.2.a.bf 5
7254.2.a.bg 5
7254.2.a.bh 5
7254.2.a.bi 6
7254.2.a.bj 6
7254.2.a.bk 6
7254.2.a.bl 6
7254.2.a.bm 6
7254.2.a.bn 7
7254.2.a.bo 7
7254.2.a.bp 7
7254.2.a.bq 7
7254.2.a.br 7
7254.2.a.bs 7
7254.2.b \(\chi_{7254}(1117, \cdot)\) n/a 176 1
7254.2.e \(\chi_{7254}(6137, \cdot)\) n/a 128 1
7254.2.f \(\chi_{7254}(7253, \cdot)\) n/a 144 1
7254.2.i \(\chi_{7254}(1927, \cdot)\) n/a 372 2
7254.2.j \(\chi_{7254}(3043, \cdot)\) n/a 320 2
7254.2.k \(\chi_{7254}(2419, \cdot)\) n/a 720 2
7254.2.l \(\chi_{7254}(211, \cdot)\) n/a 896 2
7254.2.m \(\chi_{7254}(1327, \cdot)\) n/a 768 2
7254.2.n \(\chi_{7254}(373, \cdot)\) n/a 840 2
7254.2.o \(\chi_{7254}(4117, \cdot)\) n/a 896 2
7254.2.p \(\chi_{7254}(3721, \cdot)\) n/a 840 2
7254.2.q \(\chi_{7254}(2629, \cdot)\) n/a 372 2
7254.2.r \(\chi_{7254}(2791, \cdot)\) n/a 348 2
7254.2.s \(\chi_{7254}(3415, \cdot)\) n/a 896 2
7254.2.t \(\chi_{7254}(1699, \cdot)\) n/a 896 2
7254.2.u \(\chi_{7254}(625, \cdot)\) n/a 768 2
7254.2.x \(\chi_{7254}(125, \cdot)\) n/a 280 2
7254.2.y \(\chi_{7254}(5455, \cdot)\) n/a 368 2
7254.2.z \(\chi_{7254}(469, \cdot)\) n/a 640 4
7254.2.bb \(\chi_{7254}(25, \cdot)\) n/a 896 2
7254.2.bd \(\chi_{7254}(1673, \cdot)\) n/a 304 2
7254.2.be \(\chi_{7254}(1049, \cdot)\) n/a 896 2
7254.2.bh \(\chi_{7254}(2765, \cdot)\) n/a 896 2
7254.2.bi \(\chi_{7254}(2857, \cdot)\) n/a 896 2
7254.2.bl \(\chi_{7254}(2233, \cdot)\) n/a 352 2
7254.2.bm \(\chi_{7254}(1141, \cdot)\) n/a 896 2
7254.2.bo \(\chi_{7254}(5513, \cdot)\) n/a 768 2
7254.2.bq \(\chi_{7254}(1421, \cdot)\) n/a 296 2
7254.2.bt \(\chi_{7254}(2909, \cdot)\) n/a 896 2
7254.2.bu \(\chi_{7254}(2045, \cdot)\) n/a 896 2
7254.2.cc \(\chi_{7254}(1793, \cdot)\) n/a 896 2
7254.2.cd \(\chi_{7254}(5951, \cdot)\) n/a 896 2
7254.2.ci \(\chi_{7254}(719, \cdot)\) n/a 296 2
7254.2.cj \(\chi_{7254}(3509, \cdot)\) n/a 304 2
7254.2.ck \(\chi_{7254}(2417, \cdot)\) n/a 896 2
7254.2.cl \(\chi_{7254}(6257, \cdot)\) n/a 896 2
7254.2.cr \(\chi_{7254}(1369, \cdot)\) n/a 372 2
7254.2.cu \(\chi_{7254}(439, \cdot)\) n/a 896 2
7254.2.cv \(\chi_{7254}(745, \cdot)\) n/a 840 2
7254.2.cz \(\chi_{7254}(1979, \cdot)\) n/a 296 2
7254.2.da \(\chi_{7254}(2393, \cdot)\) n/a 256 2
7254.2.db \(\chi_{7254}(1301, \cdot)\) n/a 768 2
7254.2.dc \(\chi_{7254}(3467, \cdot)\) n/a 896 2
7254.2.dh \(\chi_{7254}(677, \cdot)\) n/a 768 2
7254.2.di \(\chi_{7254}(2603, \cdot)\) n/a 896 2
7254.2.dj \(\chi_{7254}(2443, \cdot)\) n/a 896 2
7254.2.dk \(\chi_{7254}(3163, \cdot)\) n/a 840 2
7254.2.dp \(\chi_{7254}(2071, \cdot)\) n/a 372 2
7254.2.dq \(\chi_{7254}(4159, \cdot)\) n/a 376 2
7254.2.dr \(\chi_{7254}(3535, \cdot)\) n/a 840 2
7254.2.ds \(\chi_{7254}(3559, \cdot)\) n/a 896 2
7254.2.dw \(\chi_{7254}(347, \cdot)\) n/a 896 2
7254.2.dx \(\chi_{7254}(185, \cdot)\) n/a 896 2
7254.2.ea \(\chi_{7254}(1277, \cdot)\) n/a 296 2
7254.2.ec \(\chi_{7254}(1091, \cdot)\) n/a 896 2
7254.2.eg \(\chi_{7254}(491, \cdot)\) n/a 896 2
7254.2.ej \(\chi_{7254}(1115, \cdot)\) n/a 304 2
7254.2.ek \(\chi_{7254}(2207, \cdot)\) n/a 896 2
7254.2.en \(\chi_{7254}(2627, \cdot)\) n/a 512 4
7254.2.eq \(\chi_{7254}(1585, \cdot)\) n/a 736 4
7254.2.et \(\chi_{7254}(3743, \cdot)\) n/a 576 4
7254.2.fc \(\chi_{7254}(5, \cdot)\) n/a 1792 4
7254.2.fd \(\chi_{7254}(1549, \cdot)\) n/a 752 4
7254.2.fe \(\chi_{7254}(683, \cdot)\) n/a 560 4
7254.2.ff \(\chi_{7254}(1669, \cdot)\) n/a 1792 4
7254.2.fg \(\chi_{7254}(3595, \cdot)\) n/a 1792 4
7254.2.fh \(\chi_{7254}(409, \cdot)\) n/a 1792 4
7254.2.fi \(\chi_{7254}(149, \cdot)\) n/a 1792 4
7254.2.fj \(\chi_{7254}(1055, \cdot)\) n/a 1680 4
7254.2.fk \(\chi_{7254}(707, \cdot)\) n/a 1792 4
7254.2.fl \(\chi_{7254}(739, \cdot)\) n/a 744 4
7254.2.fm \(\chi_{7254}(1493, \cdot)\) n/a 592 4
7254.2.fn \(\chi_{7254}(967, \cdot)\) n/a 1792 4
7254.2.fo \(\chi_{7254}(3343, \cdot)\) n/a 1792 4
7254.2.fp \(\chi_{7254}(1679, \cdot)\) n/a 1792 4
7254.2.fq \(\chi_{7254}(3167, \cdot)\) n/a 608 4
7254.2.fr \(\chi_{7254}(1711, \cdot)\) n/a 752 4
7254.2.fs \(\chi_{7254}(1177, \cdot)\) n/a 1792 4
7254.2.ft \(\chi_{7254}(869, \cdot)\) n/a 1680 4
7254.2.gm \(\chi_{7254}(223, \cdot)\) n/a 1792 4
7254.2.gn \(\chi_{7254}(4799, \cdot)\) n/a 1792 4
7254.2.go \(\chi_{7254}(2543, \cdot)\) n/a 1680 4
7254.2.gp \(\chi_{7254}(37, \cdot)\) n/a 744 4
7254.2.gq \(\chi_{7254}(2195, \cdot)\) n/a 592 4
7254.2.gr \(\chi_{7254}(619, \cdot)\) n/a 1792 4
7254.2.gs \(\chi_{7254}(2641, \cdot)\) n/a 1792 4
7254.2.gt \(\chi_{7254}(1307, \cdot)\) n/a 1792 4
7254.2.gu \(\chi_{7254}(919, \cdot)\) n/a 1488 8
7254.2.gv \(\chi_{7254}(295, \cdot)\) n/a 3584 8
7254.2.gw \(\chi_{7254}(133, \cdot)\) n/a 3584 8
7254.2.gx \(\chi_{7254}(841, \cdot)\) n/a 3584 8
7254.2.gy \(\chi_{7254}(391, \cdot)\) n/a 3072 8
7254.2.gz \(\chi_{7254}(679, \cdot)\) n/a 3584 8
7254.2.ha \(\chi_{7254}(157, \cdot)\) n/a 3072 8
7254.2.hb \(\chi_{7254}(235, \cdot)\) n/a 1280 8
7254.2.hc \(\chi_{7254}(289, \cdot)\) n/a 1488 8
7254.2.hd \(\chi_{7254}(2965, \cdot)\) n/a 3072 8
7254.2.he \(\chi_{7254}(763, \cdot)\) n/a 3584 8
7254.2.hf \(\chi_{7254}(607, \cdot)\) n/a 3584 8
7254.2.hg \(\chi_{7254}(1225, \cdot)\) n/a 1504 8
7254.2.hh \(\chi_{7254}(1945, \cdot)\) n/a 1472 8
7254.2.hi \(\chi_{7254}(593, \cdot)\) n/a 1152 8
7254.2.hm \(\chi_{7254}(911, \cdot)\) n/a 3072 8
7254.2.ho \(\chi_{7254}(205, \cdot)\) n/a 3584 8
7254.2.hp \(\chi_{7254}(667, \cdot)\) n/a 1504 8
7254.2.hs \(\chi_{7254}(49, \cdot)\) n/a 3584 8
7254.2.ht \(\chi_{7254}(1355, \cdot)\) n/a 3584 8
7254.2.hw \(\chi_{7254}(1667, \cdot)\) n/a 3584 8
7254.2.hx \(\chi_{7254}(1205, \cdot)\) n/a 1216 8
7254.2.hz \(\chi_{7254}(103, \cdot)\) n/a 3584 8
7254.2.ig \(\chi_{7254}(641, \cdot)\) n/a 3584 8
7254.2.ih \(\chi_{7254}(77, \cdot)\) n/a 3584 8
7254.2.ii \(\chi_{7254}(1169, \cdot)\) n/a 1216 8
7254.2.ij \(\chi_{7254}(17, \cdot)\) n/a 1184 8
7254.2.io \(\chi_{7254}(2441, \cdot)\) n/a 3584 8
7254.2.ip \(\chi_{7254}(1481, \cdot)\) n/a 3584 8
7254.2.ix \(\chi_{7254}(23, \cdot)\) n/a 3584 8
7254.2.iy \(\chi_{7254}(569, \cdot)\) n/a 3584 8
7254.2.jb \(\chi_{7254}(179, \cdot)\) n/a 1184 8
7254.2.jc \(\chi_{7254}(269, \cdot)\) n/a 1184 8
7254.2.jf \(\chi_{7254}(2999, \cdot)\) n/a 3584 8
7254.2.jg \(\chi_{7254}(1199, \cdot)\) n/a 3584 8
7254.2.jk \(\chi_{7254}(751, \cdot)\) n/a 3584 8
7254.2.jl \(\chi_{7254}(1039, \cdot)\) n/a 3584 8
7254.2.jm \(\chi_{7254}(1351, \cdot)\) n/a 1504 8
7254.2.jn \(\chi_{7254}(361, \cdot)\) n/a 1488 8
7254.2.js \(\chi_{7254}(907, \cdot)\) n/a 3584 8
7254.2.jt \(\chi_{7254}(1507, \cdot)\) n/a 3584 8
7254.2.ju \(\chi_{7254}(29, \cdot)\) n/a 3584 8
7254.2.jv \(\chi_{7254}(365, \cdot)\) n/a 3072 8
7254.2.ka \(\chi_{7254}(425, \cdot)\) n/a 3584 8
7254.2.kb \(\chi_{7254}(209, \cdot)\) n/a 3072 8
7254.2.kc \(\chi_{7254}(53, \cdot)\) n/a 1024 8
7254.2.kd \(\chi_{7254}(737, \cdot)\) n/a 1184 8
7254.2.kh \(\chi_{7254}(283, \cdot)\) n/a 3584 8
7254.2.ki \(\chi_{7254}(121, \cdot)\) n/a 3584 8
7254.2.kl \(\chi_{7254}(3169, \cdot)\) n/a 1488 8
7254.2.ko \(\chi_{7254}(797, \cdot)\) n/a 3584 8
7254.2.kp \(\chi_{7254}(647, \cdot)\) n/a 1216 8
7254.2.ks \(\chi_{7254}(1109, \cdot)\) n/a 3584 8
7254.2.kw \(\chi_{7254}(389, \cdot)\) n/a 3584 8
7254.2.ky \(\chi_{7254}(227, \cdot)\) n/a 7168 16
7254.2.kz \(\chi_{7254}(331, \cdot)\) n/a 7168 16
7254.2.la \(\chi_{7254}(245, \cdot)\) n/a 7168 16
7254.2.lb \(\chi_{7254}(1159, \cdot)\) n/a 7168 16
7254.2.lc \(\chi_{7254}(151, \cdot)\) n/a 7168 16
7254.2.ld \(\chi_{7254}(71, \cdot)\) n/a 2368 16
7254.2.le \(\chi_{7254}(487, \cdot)\) n/a 2976 16
7254.2.lf \(\chi_{7254}(47, \cdot)\) n/a 7168 16
7254.2.ly \(\chi_{7254}(41, \cdot)\) n/a 7168 16
7254.2.lz \(\chi_{7254}(241, \cdot)\) n/a 7168 16
7254.2.ma \(\chi_{7254}(605, \cdot)\) n/a 7168 16
7254.2.mb \(\chi_{7254}(709, \cdot)\) n/a 7168 16
7254.2.mc \(\chi_{7254}(73, \cdot)\) n/a 3008 16
7254.2.md \(\chi_{7254}(359, \cdot)\) n/a 2432 16
7254.2.me \(\chi_{7254}(1357, \cdot)\) n/a 7168 16
7254.2.mf \(\chi_{7254}(791, \cdot)\) n/a 2432 16
7254.2.mg \(\chi_{7254}(271, \cdot)\) n/a 3008 16
7254.2.mh \(\chi_{7254}(317, \cdot)\) n/a 7168 16
7254.2.mi \(\chi_{7254}(229, \cdot)\) n/a 7168 16
7254.2.mj \(\chi_{7254}(1601, \cdot)\) n/a 2368 16
7254.2.mk \(\chi_{7254}(145, \cdot)\) n/a 2976 16
7254.2.ml \(\chi_{7254}(785, \cdot)\) n/a 7168 16
7254.2.mm \(\chi_{7254}(1523, \cdot)\) n/a 7168 16
7254.2.mn \(\chi_{7254}(59, \cdot)\) n/a 7168 16
7254.2.mo \(\chi_{7254}(115, \cdot)\) n/a 7168 16
7254.2.mp \(\chi_{7254}(85, \cdot)\) n/a 7168 16

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

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_1(7254))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_1(7254)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_1(1))\)\(^{\oplus 24}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(2))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(3))\)\(^{\oplus 16}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(6))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(9))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(13))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(18))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(26))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(31))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(39))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(62))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(78))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(93))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(117))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(186))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(234))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(279))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(403))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(558))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(806))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(1209))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(2418))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(3627))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(7254))\)\(^{\oplus 1}\)