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Properties

Label 7448.2
Level 7448
Weight 2
Dimension 905709
Nonzero newspaces 96
Sturm bound 6773760

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Defining parameters

Level: \( N \) = \( 7448 = 2^{3} \cdot 7^{2} \cdot 19 \)
Weight: \( k \) = \( 2 \)
Nonzero newspaces: \( 96 \)
Sturm bound: \(6773760\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_1(7448))\).

Total New Old
Modular forms 1706400 912305 794095
Cusp forms 1680481 905709 774772
Eisenstein series 25919 6596 19323

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_1(7448))\)

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
7448.2.a \(\chi_{7448}(1, \cdot)\) 7448.2.a.a 1 1
7448.2.a.b 1
7448.2.a.c 1
7448.2.a.d 1
7448.2.a.e 1
7448.2.a.f 1
7448.2.a.g 1
7448.2.a.h 1
7448.2.a.i 1
7448.2.a.j 1
7448.2.a.k 1
7448.2.a.l 1
7448.2.a.m 1
7448.2.a.n 1
7448.2.a.o 1
7448.2.a.p 1
7448.2.a.q 1
7448.2.a.r 1
7448.2.a.s 1
7448.2.a.t 1
7448.2.a.u 1
7448.2.a.v 1
7448.2.a.w 2
7448.2.a.x 2
7448.2.a.y 2
7448.2.a.z 2
7448.2.a.ba 2
7448.2.a.bb 2
7448.2.a.bc 2
7448.2.a.bd 2
7448.2.a.be 2
7448.2.a.bf 3
7448.2.a.bg 3
7448.2.a.bh 3
7448.2.a.bi 3
7448.2.a.bj 4
7448.2.a.bk 4
7448.2.a.bl 5
7448.2.a.bm 6
7448.2.a.bn 6
7448.2.a.bo 7
7448.2.a.bp 7
7448.2.a.bq 8
7448.2.a.br 8
7448.2.a.bs 11
7448.2.a.bt 11
7448.2.a.bu 14
7448.2.a.bv 14
7448.2.a.bw 14
7448.2.a.bx 14
7448.2.b \(\chi_{7448}(3725, \cdot)\) n/a 738 1
7448.2.e \(\chi_{7448}(6763, \cdot)\) n/a 810 1
7448.2.f \(\chi_{7448}(1861, \cdot)\) n/a 792 1
7448.2.i \(\chi_{7448}(2547, \cdot)\) n/a 720 1
7448.2.j \(\chi_{7448}(6271, \cdot)\) None 0 1
7448.2.m \(\chi_{7448}(5585, \cdot)\) n/a 200 1
7448.2.n \(\chi_{7448}(3039, \cdot)\) None 0 1
7448.2.q \(\chi_{7448}(3497, \cdot)\) n/a 360 2
7448.2.r \(\chi_{7448}(1569, \cdot)\) n/a 410 2
7448.2.s \(\chi_{7448}(3313, \cdot)\) n/a 400 2
7448.2.t \(\chi_{7448}(961, \cdot)\) n/a 400 2
7448.2.u \(\chi_{7448}(2971, \cdot)\) n/a 1584 2
7448.2.x \(\chi_{7448}(901, \cdot)\) n/a 1584 2
7448.2.y \(\chi_{7448}(4587, \cdot)\) n/a 1584 2
7448.2.bb \(\chi_{7448}(3693, \cdot)\) n/a 1584 2
7448.2.bc \(\chi_{7448}(521, \cdot)\) n/a 400 2
7448.2.bf \(\chi_{7448}(3351, \cdot)\) None 0 2
7448.2.bh \(\chi_{7448}(1471, \cdot)\) None 0 2
7448.2.bj \(\chi_{7448}(2431, \cdot)\) None 0 2
7448.2.bn \(\chi_{7448}(391, \cdot)\) None 0 2
7448.2.bp \(\chi_{7448}(2089, \cdot)\) n/a 400 2
7448.2.bq \(\chi_{7448}(2775, \cdot)\) None 0 2
7448.2.bs \(\chi_{7448}(1665, \cdot)\) n/a 400 2
7448.2.bw \(\chi_{7448}(4967, \cdot)\) None 0 2
7448.2.bx \(\chi_{7448}(1243, \cdot)\) n/a 1584 2
7448.2.ca \(\chi_{7448}(1341, \cdot)\) n/a 1584 2
7448.2.cc \(\chi_{7448}(293, \cdot)\) n/a 1584 2
7448.2.ce \(\chi_{7448}(3155, \cdot)\) n/a 1440 2
7448.2.cf \(\chi_{7448}(2469, \cdot)\) n/a 1584 2
7448.2.ch \(\chi_{7448}(4115, \cdot)\) n/a 1584 2
7448.2.ck \(\chi_{7448}(197, \cdot)\) n/a 1620 2
7448.2.cm \(\chi_{7448}(2811, \cdot)\) n/a 1584 2
7448.2.cn \(\chi_{7448}(3117, \cdot)\) n/a 1440 2
7448.2.cp \(\chi_{7448}(2843, \cdot)\) n/a 1620 2
7448.2.cr \(\chi_{7448}(619, \cdot)\) n/a 1584 2
7448.2.cu \(\chi_{7448}(4245, \cdot)\) n/a 1584 2
7448.2.cx \(\chi_{7448}(863, \cdot)\) None 0 2
7448.2.cy \(\chi_{7448}(4625, \cdot)\) n/a 400 2
7448.2.db \(\chi_{7448}(999, \cdot)\) None 0 2
7448.2.dc \(\chi_{7448}(1065, \cdot)\) n/a 1512 6
7448.2.dd \(\chi_{7448}(785, \cdot)\) n/a 1230 6
7448.2.de \(\chi_{7448}(177, \cdot)\) n/a 1200 6
7448.2.df \(\chi_{7448}(1745, \cdot)\) n/a 1200 6
7448.2.di \(\chi_{7448}(911, \cdot)\) None 0 6
7448.2.dj \(\chi_{7448}(265, \cdot)\) n/a 1680 6
7448.2.dm \(\chi_{7448}(951, \cdot)\) None 0 6
7448.2.dn \(\chi_{7448}(419, \cdot)\) n/a 6048 6
7448.2.dq \(\chi_{7448}(797, \cdot)\) n/a 6696 6
7448.2.dr \(\chi_{7448}(379, \cdot)\) n/a 6696 6
7448.2.du \(\chi_{7448}(533, \cdot)\) n/a 6048 6
7448.2.dv \(\chi_{7448}(1783, \cdot)\) None 0 6
7448.2.dw \(\chi_{7448}(79, \cdot)\) None 0 6
7448.2.dz \(\chi_{7448}(117, \cdot)\) n/a 4752 6
7448.2.ea \(\chi_{7448}(557, \cdot)\) n/a 4752 6
7448.2.ef \(\chi_{7448}(97, \cdot)\) n/a 1200 6
7448.2.ei \(\chi_{7448}(3449, \cdot)\) n/a 1200 6
7448.2.el \(\chi_{7448}(195, \cdot)\) n/a 4752 6
7448.2.em \(\chi_{7448}(1275, \cdot)\) n/a 4860 6
7448.2.ep \(\chi_{7448}(459, \cdot)\) n/a 4752 6
7448.2.eq \(\chi_{7448}(1403, \cdot)\) n/a 4752 6
7448.2.et \(\chi_{7448}(295, \cdot)\) None 0 6
7448.2.eu \(\chi_{7448}(783, \cdot)\) None 0 6
7448.2.ex \(\chi_{7448}(215, \cdot)\) None 0 6
7448.2.ey \(\chi_{7448}(471, \cdot)\) None 0 6
7448.2.fb \(\chi_{7448}(1373, \cdot)\) n/a 4860 6
7448.2.fc \(\chi_{7448}(1077, \cdot)\) n/a 4752 6
7448.2.ff \(\chi_{7448}(325, \cdot)\) n/a 4752 6
7448.2.fg \(\chi_{7448}(2125, \cdot)\) n/a 4752 6
7448.2.fh \(\chi_{7448}(129, \cdot)\) n/a 1200 6
7448.2.fk \(\chi_{7448}(67, \cdot)\) n/a 4752 6
7448.2.fl \(\chi_{7448}(803, \cdot)\) n/a 4752 6
7448.2.fo \(\chi_{7448}(1033, \cdot)\) n/a 3360 12
7448.2.fp \(\chi_{7448}(121, \cdot)\) n/a 3360 12
7448.2.fq \(\chi_{7448}(505, \cdot)\) n/a 3360 12
7448.2.fr \(\chi_{7448}(305, \cdot)\) n/a 3024 12
7448.2.fs \(\chi_{7448}(311, \cdot)\) None 0 12
7448.2.fv \(\chi_{7448}(297, \cdot)\) n/a 3360 12
7448.2.fw \(\chi_{7448}(487, \cdot)\) None 0 12
7448.2.fz \(\chi_{7448}(677, \cdot)\) n/a 13392 12
7448.2.gc \(\chi_{7448}(691, \cdot)\) n/a 13392 12
7448.2.ge \(\chi_{7448}(715, \cdot)\) n/a 13392 12
7448.2.gg \(\chi_{7448}(837, \cdot)\) n/a 12096 12
7448.2.gh \(\chi_{7448}(683, \cdot)\) n/a 13392 12
7448.2.gj \(\chi_{7448}(1037, \cdot)\) n/a 13392 12
7448.2.gm \(\chi_{7448}(83, \cdot)\) n/a 13392 12
7448.2.go \(\chi_{7448}(341, \cdot)\) n/a 13392 12
7448.2.gp \(\chi_{7448}(115, \cdot)\) n/a 12096 12
7448.2.gr \(\chi_{7448}(69, \cdot)\) n/a 13392 12
7448.2.gt \(\chi_{7448}(277, \cdot)\) n/a 13392 12
7448.2.gw \(\chi_{7448}(107, \cdot)\) n/a 13392 12
7448.2.gx \(\chi_{7448}(639, \cdot)\) None 0 12
7448.2.hb \(\chi_{7448}(601, \cdot)\) n/a 3360 12
7448.2.hd \(\chi_{7448}(495, \cdot)\) None 0 12
7448.2.he \(\chi_{7448}(873, \cdot)\) n/a 3360 12
7448.2.hg \(\chi_{7448}(615, \cdot)\) None 0 12
7448.2.hk \(\chi_{7448}(151, \cdot)\) None 0 12
7448.2.hm \(\chi_{7448}(183, \cdot)\) None 0 12
7448.2.ho \(\chi_{7448}(87, \cdot)\) None 0 12
7448.2.hr \(\chi_{7448}(145, \cdot)\) n/a 3360 12
7448.2.hs \(\chi_{7448}(429, \cdot)\) n/a 13392 12
7448.2.hv \(\chi_{7448}(331, \cdot)\) n/a 13392 12
7448.2.hw \(\chi_{7448}(829, \cdot)\) n/a 13392 12
7448.2.hz \(\chi_{7448}(467, \cdot)\) n/a 13392 12
7448.2.ia \(\chi_{7448}(25, \cdot)\) n/a 10080 36
7448.2.ib \(\chi_{7448}(169, \cdot)\) n/a 10080 36
7448.2.ic \(\chi_{7448}(9, \cdot)\) n/a 10080 36
7448.2.id \(\chi_{7448}(131, \cdot)\) n/a 40176 36
7448.2.ie \(\chi_{7448}(611, \cdot)\) n/a 40176 36
7448.2.ih \(\chi_{7448}(33, \cdot)\) n/a 10080 36
7448.2.im \(\chi_{7448}(13, \cdot)\) n/a 40176 36
7448.2.in \(\chi_{7448}(85, \cdot)\) n/a 40176 36
7448.2.iq \(\chi_{7448}(541, \cdot)\) n/a 40176 36
7448.2.ir \(\chi_{7448}(269, \cdot)\) n/a 40176 36
7448.2.iu \(\chi_{7448}(55, \cdot)\) None 0 36
7448.2.iv \(\chi_{7448}(15, \cdot)\) None 0 36
7448.2.iy \(\chi_{7448}(375, \cdot)\) None 0 36
7448.2.iz \(\chi_{7448}(47, \cdot)\) None 0 36
7448.2.jc \(\chi_{7448}(155, \cdot)\) n/a 40176 36
7448.2.jd \(\chi_{7448}(139, \cdot)\) n/a 40176 36
7448.2.jg \(\chi_{7448}(283, \cdot)\) n/a 40176 36
7448.2.jh \(\chi_{7448}(51, \cdot)\) n/a 40176 36
7448.2.jk \(\chi_{7448}(41, \cdot)\) n/a 10080 36
7448.2.jn \(\chi_{7448}(89, \cdot)\) n/a 10080 36
7448.2.jo \(\chi_{7448}(93, \cdot)\) n/a 40176 36
7448.2.jp \(\chi_{7448}(173, \cdot)\) n/a 40176 36
7448.2.js \(\chi_{7448}(135, \cdot)\) None 0 36
7448.2.jt \(\chi_{7448}(199, \cdot)\) None 0 36

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

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_1(7448))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_1(7448)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_1(1))\)\(^{\oplus 24}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(2))\)\(^{\oplus 18}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(4))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(7))\)\(^{\oplus 16}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(8))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(14))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(19))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(28))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(38))\)\(^{\oplus 9}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(49))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(56))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(76))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(98))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(133))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(152))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(196))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(266))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(392))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(532))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(931))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(1064))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(1862))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(3724))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(7448))\)\(^{\oplus 1}\)