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Properties

Label 7245.2
Level 7245
Weight 2
Dimension 1258572
Nonzero newspaces 120
Sturm bound 7299072

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Defining parameters

Level: \( N \) = \( 7245 = 3^{2} \cdot 5 \cdot 7 \cdot 23 \)
Weight: \( k \) = \( 2 \)
Nonzero newspaces: \( 120 \)
Sturm bound: \(7299072\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_1(7245))\).

Total New Old
Modular forms 1841664 1269908 571756
Cusp forms 1807873 1258572 549301
Eisenstein series 33791 11336 22455

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_1(7245))\)

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
7245.2.a \(\chi_{7245}(1, \cdot)\) 7245.2.a.a 1 1
7245.2.a.b 1
7245.2.a.c 1
7245.2.a.d 1
7245.2.a.e 1
7245.2.a.f 1
7245.2.a.g 1
7245.2.a.h 1
7245.2.a.i 1
7245.2.a.j 1
7245.2.a.k 1
7245.2.a.l 1
7245.2.a.m 1
7245.2.a.n 1
7245.2.a.o 1
7245.2.a.p 1
7245.2.a.q 1
7245.2.a.r 1
7245.2.a.s 1
7245.2.a.t 1
7245.2.a.u 1
7245.2.a.v 2
7245.2.a.w 2
7245.2.a.x 2
7245.2.a.y 3
7245.2.a.z 3
7245.2.a.ba 3
7245.2.a.bb 3
7245.2.a.bc 4
7245.2.a.bd 4
7245.2.a.be 4
7245.2.a.bf 4
7245.2.a.bg 5
7245.2.a.bh 5
7245.2.a.bi 5
7245.2.a.bj 6
7245.2.a.bk 6
7245.2.a.bl 7
7245.2.a.bm 7
7245.2.a.bn 7
7245.2.a.bo 8
7245.2.a.bp 8
7245.2.a.bq 8
7245.2.a.br 9
7245.2.a.bs 9
7245.2.a.bt 9
7245.2.a.bu 10
7245.2.a.bv 10
7245.2.a.bw 10
7245.2.a.bx 10
7245.2.a.by 13
7245.2.a.bz 13
7245.2.b \(\chi_{7245}(5291, \cdot)\) n/a 240 1
7245.2.e \(\chi_{7245}(4024, \cdot)\) n/a 476 1
7245.2.g \(\chi_{7245}(2899, \cdot)\) n/a 332 1
7245.2.h \(\chi_{7245}(2276, \cdot)\) n/a 192 1
7245.2.k \(\chi_{7245}(1126, \cdot)\) n/a 320 1
7245.2.l \(\chi_{7245}(944, \cdot)\) n/a 352 1
7245.2.n \(\chi_{7245}(5174, \cdot)\) n/a 288 1
7245.2.q \(\chi_{7245}(2416, \cdot)\) n/a 1056 2
7245.2.r \(\chi_{7245}(4141, \cdot)\) n/a 584 2
7245.2.s \(\chi_{7245}(3796, \cdot)\) n/a 1408 2
7245.2.t \(\chi_{7245}(1381, \cdot)\) n/a 1408 2
7245.2.v \(\chi_{7245}(323, \cdot)\) n/a 528 2
7245.2.w \(\chi_{7245}(3403, \cdot)\) n/a 720 2
7245.2.z \(\chi_{7245}(1448, \cdot)\) n/a 768 2
7245.2.ba \(\chi_{7245}(622, \cdot)\) n/a 880 2
7245.2.bd \(\chi_{7245}(1586, \cdot)\) n/a 1536 2
7245.2.be \(\chi_{7245}(4279, \cdot)\) n/a 2112 2
7245.2.bg \(\chi_{7245}(229, \cdot)\) n/a 2288 2
7245.2.bj \(\chi_{7245}(3566, \cdot)\) n/a 1408 2
7245.2.bl \(\chi_{7245}(1634, \cdot)\) n/a 2112 2
7245.2.bm \(\chi_{7245}(6646, \cdot)\) n/a 1536 2
7245.2.bo \(\chi_{7245}(2069, \cdot)\) n/a 768 2
7245.2.bs \(\chi_{7245}(344, \cdot)\) n/a 1728 2
7245.2.bv \(\chi_{7245}(2161, \cdot)\) n/a 640 2
7245.2.bx \(\chi_{7245}(3359, \cdot)\) n/a 2112 2
7245.2.by \(\chi_{7245}(3541, \cdot)\) n/a 1536 2
7245.2.ca \(\chi_{7245}(1979, \cdot)\) n/a 704 2
7245.2.ce \(\chi_{7245}(6554, \cdot)\) n/a 2288 2
7245.2.cf \(\chi_{7245}(2299, \cdot)\) n/a 2288 2
7245.2.ci \(\chi_{7245}(1496, \cdot)\) n/a 1408 2
7245.2.ck \(\chi_{7245}(1864, \cdot)\) n/a 880 2
7245.2.cm \(\chi_{7245}(4691, \cdot)\) n/a 1152 2
7245.2.cn \(\chi_{7245}(484, \cdot)\) n/a 1584 2
7245.2.cp \(\chi_{7245}(1241, \cdot)\) n/a 512 2
7245.2.cr \(\chi_{7245}(1151, \cdot)\) n/a 464 2
7245.2.ct \(\chi_{7245}(1609, \cdot)\) n/a 2288 2
7245.2.cw \(\chi_{7245}(461, \cdot)\) n/a 1408 2
7245.2.cy \(\chi_{7245}(5059, \cdot)\) n/a 952 2
7245.2.da \(\chi_{7245}(3656, \cdot)\) n/a 1536 2
7245.2.db \(\chi_{7245}(2209, \cdot)\) n/a 2112 2
7245.2.df \(\chi_{7245}(1724, \cdot)\) n/a 2288 2
7245.2.dh \(\chi_{7245}(6464, \cdot)\) n/a 2112 2
7245.2.di \(\chi_{7245}(1816, \cdot)\) n/a 1536 2
7245.2.dk \(\chi_{7245}(946, \cdot)\) n/a 2400 10
7245.2.dm \(\chi_{7245}(1312, \cdot)\) n/a 4224 4
7245.2.dn \(\chi_{7245}(68, \cdot)\) n/a 4576 4
7245.2.dq \(\chi_{7245}(4783, \cdot)\) n/a 4576 4
7245.2.dr \(\chi_{7245}(1082, \cdot)\) n/a 4224 4
7245.2.du \(\chi_{7245}(1402, \cdot)\) n/a 4576 4
7245.2.dv \(\chi_{7245}(1703, \cdot)\) n/a 4224 4
7245.2.dx \(\chi_{7245}(482, \cdot)\) n/a 4576 4
7245.2.dz \(\chi_{7245}(208, \cdot)\) n/a 1760 4
7245.2.ec \(\chi_{7245}(2483, \cdot)\) n/a 1536 4
7245.2.ee \(\chi_{7245}(1588, \cdot)\) n/a 4224 4
7245.2.ef \(\chi_{7245}(2738, \cdot)\) n/a 3168 4
7245.2.eh \(\chi_{7245}(298, \cdot)\) n/a 1904 4
7245.2.ek \(\chi_{7245}(737, \cdot)\) n/a 1408 4
7245.2.em \(\chi_{7245}(22, \cdot)\) n/a 3456 4
7245.2.eo \(\chi_{7245}(4693, \cdot)\) n/a 4224 4
7245.2.ep \(\chi_{7245}(2138, \cdot)\) n/a 4576 4
7245.2.et \(\chi_{7245}(134, \cdot)\) n/a 2880 10
7245.2.ev \(\chi_{7245}(629, \cdot)\) n/a 3840 10
7245.2.ew \(\chi_{7245}(181, \cdot)\) n/a 3200 10
7245.2.ez \(\chi_{7245}(701, \cdot)\) n/a 1920 10
7245.2.fa \(\chi_{7245}(64, \cdot)\) n/a 3600 10
7245.2.fc \(\chi_{7245}(244, \cdot)\) n/a 4760 10
7245.2.ff \(\chi_{7245}(1511, \cdot)\) n/a 2560 10
7245.2.fg \(\chi_{7245}(121, \cdot)\) n/a 15360 20
7245.2.fh \(\chi_{7245}(16, \cdot)\) n/a 15360 20
7245.2.fi \(\chi_{7245}(361, \cdot)\) n/a 6400 20
7245.2.fj \(\chi_{7245}(211, \cdot)\) n/a 11520 20
7245.2.fl \(\chi_{7245}(118, \cdot)\) n/a 9520 20
7245.2.fm \(\chi_{7245}(503, \cdot)\) n/a 7680 20
7245.2.fp \(\chi_{7245}(442, \cdot)\) n/a 7200 20
7245.2.fq \(\chi_{7245}(8, \cdot)\) n/a 5760 20
7245.2.ft \(\chi_{7245}(166, \cdot)\) n/a 15360 20
7245.2.fu \(\chi_{7245}(164, \cdot)\) n/a 22880 20
7245.2.fw \(\chi_{7245}(74, \cdot)\) n/a 22880 20
7245.2.ga \(\chi_{7245}(4, \cdot)\) n/a 22880 20
7245.2.gb \(\chi_{7245}(191, \cdot)\) n/a 15360 20
7245.2.gd \(\chi_{7245}(19, \cdot)\) n/a 9520 20
7245.2.gf \(\chi_{7245}(41, \cdot)\) n/a 15360 20
7245.2.gi \(\chi_{7245}(34, \cdot)\) n/a 22880 20
7245.2.gk \(\chi_{7245}(26, \cdot)\) n/a 5120 20
7245.2.gm \(\chi_{7245}(296, \cdot)\) n/a 5120 20
7245.2.go \(\chi_{7245}(169, \cdot)\) n/a 17280 20
7245.2.gp \(\chi_{7245}(176, \cdot)\) n/a 11520 20
7245.2.gr \(\chi_{7245}(289, \cdot)\) n/a 9520 20
7245.2.gt \(\chi_{7245}(236, \cdot)\) n/a 15360 20
7245.2.gw \(\chi_{7245}(724, \cdot)\) n/a 22880 20
7245.2.gx \(\chi_{7245}(569, \cdot)\) n/a 22880 20
7245.2.hb \(\chi_{7245}(269, \cdot)\) n/a 7680 20
7245.2.hd \(\chi_{7245}(76, \cdot)\) n/a 15360 20
7245.2.he \(\chi_{7245}(104, \cdot)\) n/a 22880 20
7245.2.hg \(\chi_{7245}(136, \cdot)\) n/a 6400 20
7245.2.hj \(\chi_{7245}(659, \cdot)\) n/a 17280 20
7245.2.hn \(\chi_{7245}(44, \cdot)\) n/a 7680 20
7245.2.hp \(\chi_{7245}(61, \cdot)\) n/a 15360 20
7245.2.hq \(\chi_{7245}(59, \cdot)\) n/a 22880 20
7245.2.hs \(\chi_{7245}(101, \cdot)\) n/a 15360 20
7245.2.hv \(\chi_{7245}(304, \cdot)\) n/a 22880 20
7245.2.hx \(\chi_{7245}(499, \cdot)\) n/a 22880 20
7245.2.hy \(\chi_{7245}(11, \cdot)\) n/a 15360 20
7245.2.ib \(\chi_{7245}(122, \cdot)\) n/a 45760 40
7245.2.ic \(\chi_{7245}(187, \cdot)\) n/a 45760 40
7245.2.ie \(\chi_{7245}(43, \cdot)\) n/a 34560 40
7245.2.ig \(\chi_{7245}(233, \cdot)\) n/a 15360 40
7245.2.ij \(\chi_{7245}(37, \cdot)\) n/a 19040 40
7245.2.il \(\chi_{7245}(302, \cdot)\) n/a 34560 40
7245.2.im \(\chi_{7245}(13, \cdot)\) n/a 45760 40
7245.2.io \(\chi_{7245}(17, \cdot)\) n/a 15360 40
7245.2.ir \(\chi_{7245}(73, \cdot)\) n/a 19040 40
7245.2.it \(\chi_{7245}(83, \cdot)\) n/a 45760 40
7245.2.iv \(\chi_{7245}(2, \cdot)\) n/a 45760 40
7245.2.iw \(\chi_{7245}(67, \cdot)\) n/a 45760 40
7245.2.iz \(\chi_{7245}(338, \cdot)\) n/a 45760 40
7245.2.ja \(\chi_{7245}(88, \cdot)\) n/a 45760 40
7245.2.jd \(\chi_{7245}(38, \cdot)\) n/a 45760 40
7245.2.je \(\chi_{7245}(52, \cdot)\) n/a 45760 40

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

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_1(7245))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_1(7245)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_1(15))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(21))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(23))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(35))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(45))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(63))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(69))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(105))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(115))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(161))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(207))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(315))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(345))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(483))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(805))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(1035))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(1449))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(2415))\)\(^{\oplus 2}\)