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Properties

Label 7360.2
Level 7360
Weight 2
Dimension 830412
Nonzero newspaces 56
Sturm bound 6488064

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Defining parameters

Level: \( N \) = \( 7360 = 2^{6} \cdot 5 \cdot 23 \)
Weight: \( k \) = \( 2 \)
Nonzero newspaces: \( 56 \)
Sturm bound: \(6488064\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_1(7360))\).

Total New Old
Modular forms 1634688 835956 798732
Cusp forms 1609345 830412 778933
Eisenstein series 25343 5544 19799

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_1(7360))\)

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 the newforms together with their dimension.

Label \(\chi\) Newforms Dimension \(\chi\) degree
7360.2.a \(\chi_{7360}(1, \cdot)\) 7360.2.a.a 1 1
7360.2.a.b 1
7360.2.a.c 1
7360.2.a.d 1
7360.2.a.e 1
7360.2.a.f 1
7360.2.a.g 1
7360.2.a.h 1
7360.2.a.i 1
7360.2.a.j 1
7360.2.a.k 1
7360.2.a.l 1
7360.2.a.m 1
7360.2.a.n 1
7360.2.a.o 1
7360.2.a.p 1
7360.2.a.q 1
7360.2.a.r 1
7360.2.a.s 1
7360.2.a.t 1
7360.2.a.u 1
7360.2.a.v 1
7360.2.a.w 1
7360.2.a.x 1
7360.2.a.y 1
7360.2.a.z 1
7360.2.a.ba 1
7360.2.a.bb 1
7360.2.a.bc 2
7360.2.a.bd 2
7360.2.a.be 2
7360.2.a.bf 2
7360.2.a.bg 2
7360.2.a.bh 2
7360.2.a.bi 2
7360.2.a.bj 2
7360.2.a.bk 2
7360.2.a.bl 2
7360.2.a.bm 2
7360.2.a.bn 2
7360.2.a.bo 2
7360.2.a.bp 2
7360.2.a.bq 2
7360.2.a.br 2
7360.2.a.bs 2
7360.2.a.bt 2
7360.2.a.bu 2
7360.2.a.bv 2
7360.2.a.bw 3
7360.2.a.bx 3
7360.2.a.by 3
7360.2.a.bz 3
7360.2.a.ca 3
7360.2.a.cb 3
7360.2.a.cc 3
7360.2.a.cd 3
7360.2.a.ce 3
7360.2.a.cf 3
7360.2.a.cg 4
7360.2.a.ch 4
7360.2.a.ci 4
7360.2.a.cj 4
7360.2.a.ck 5
7360.2.a.cl 5
7360.2.a.cm 5
7360.2.a.cn 5
7360.2.a.co 5
7360.2.a.cp 5
7360.2.a.cq 5
7360.2.a.cr 5
7360.2.a.cs 5
7360.2.a.ct 5
7360.2.a.cu 6
7360.2.a.cv 6
7360.2.b \(\chi_{7360}(3679, \cdot)\) n/a 288 1
7360.2.e \(\chi_{7360}(5889, \cdot)\) n/a 264 1
7360.2.f \(\chi_{7360}(3681, \cdot)\) n/a 176 1
7360.2.i \(\chi_{7360}(1471, \cdot)\) n/a 192 1
7360.2.j \(\chi_{7360}(2209, \cdot)\) n/a 264 1
7360.2.m \(\chi_{7360}(7359, \cdot)\) n/a 284 1
7360.2.n \(\chi_{7360}(5151, \cdot)\) n/a 192 1
7360.2.r \(\chi_{7360}(6577, \cdot)\) n/a 568 2
7360.2.t \(\chi_{7360}(47, \cdot)\) n/a 528 2
7360.2.u \(\chi_{7360}(3311, \cdot)\) n/a 384 2
7360.2.x \(\chi_{7360}(1841, \cdot)\) n/a 352 2
7360.2.y \(\chi_{7360}(1793, \cdot)\) n/a 568 2
7360.2.ba \(\chi_{7360}(2623, \cdot)\) n/a 528 2
7360.2.bd \(\chi_{7360}(1887, \cdot)\) n/a 528 2
7360.2.bf \(\chi_{7360}(1057, \cdot)\) n/a 576 2
7360.2.bg \(\chi_{7360}(369, \cdot)\) n/a 528 2
7360.2.bj \(\chi_{7360}(1839, \cdot)\) n/a 568 2
7360.2.bk \(\chi_{7360}(3727, \cdot)\) n/a 528 2
7360.2.bm \(\chi_{7360}(2897, \cdot)\) n/a 568 2
7360.2.bp \(\chi_{7360}(1703, \cdot)\) None 0 4
7360.2.br \(\chi_{7360}(137, \cdot)\) None 0 4
7360.2.bs \(\chi_{7360}(919, \cdot)\) None 0 4
7360.2.bu \(\chi_{7360}(921, \cdot)\) None 0 4
7360.2.bx \(\chi_{7360}(551, \cdot)\) None 0 4
7360.2.bz \(\chi_{7360}(1289, \cdot)\) None 0 4
7360.2.ca \(\chi_{7360}(967, \cdot)\) None 0 4
7360.2.cc \(\chi_{7360}(873, \cdot)\) None 0 4
7360.2.ce \(\chi_{7360}(961, \cdot)\) n/a 1920 10
7360.2.cg \(\chi_{7360}(413, \cdot)\) n/a 9184 8
7360.2.ci \(\chi_{7360}(1243, \cdot)\) n/a 8448 8
7360.2.ck \(\chi_{7360}(461, \cdot)\) n/a 5632 8
7360.2.cl \(\chi_{7360}(829, \cdot)\) n/a 8448 8
7360.2.co \(\chi_{7360}(459, \cdot)\) n/a 9184 8
7360.2.cp \(\chi_{7360}(91, \cdot)\) n/a 6144 8
7360.2.cr \(\chi_{7360}(1333, \cdot)\) n/a 9184 8
7360.2.ct \(\chi_{7360}(323, \cdot)\) n/a 8448 8
7360.2.cx \(\chi_{7360}(1631, \cdot)\) n/a 1920 10
7360.2.cy \(\chi_{7360}(319, \cdot)\) n/a 2840 10
7360.2.db \(\chi_{7360}(289, \cdot)\) n/a 2880 10
7360.2.dc \(\chi_{7360}(191, \cdot)\) n/a 1920 10
7360.2.df \(\chi_{7360}(1761, \cdot)\) n/a 1920 10
7360.2.dg \(\chi_{7360}(449, \cdot)\) n/a 2840 10
7360.2.dj \(\chi_{7360}(159, \cdot)\) n/a 2880 10
7360.2.dl \(\chi_{7360}(17, \cdot)\) n/a 5680 20
7360.2.dn \(\chi_{7360}(303, \cdot)\) n/a 5680 20
7360.2.dp \(\chi_{7360}(79, \cdot)\) n/a 5680 20
7360.2.dq \(\chi_{7360}(49, \cdot)\) n/a 5680 20
7360.2.ds \(\chi_{7360}(33, \cdot)\) n/a 5760 20
7360.2.du \(\chi_{7360}(223, \cdot)\) n/a 5760 20
7360.2.dx \(\chi_{7360}(127, \cdot)\) n/a 5680 20
7360.2.dz \(\chi_{7360}(513, \cdot)\) n/a 5680 20
7360.2.eb \(\chi_{7360}(81, \cdot)\) n/a 3840 20
7360.2.ec \(\chi_{7360}(111, \cdot)\) n/a 3840 20
7360.2.ee \(\chi_{7360}(463, \cdot)\) n/a 5680 20
7360.2.eg \(\chi_{7360}(273, \cdot)\) n/a 5680 20
7360.2.ej \(\chi_{7360}(57, \cdot)\) None 0 40
7360.2.el \(\chi_{7360}(167, \cdot)\) None 0 40
7360.2.en \(\chi_{7360}(9, \cdot)\) None 0 40
7360.2.ep \(\chi_{7360}(471, \cdot)\) None 0 40
7360.2.eq \(\chi_{7360}(41, \cdot)\) None 0 40
7360.2.es \(\chi_{7360}(199, \cdot)\) None 0 40
7360.2.eu \(\chi_{7360}(153, \cdot)\) None 0 40
7360.2.ew \(\chi_{7360}(87, \cdot)\) None 0 40
7360.2.ey \(\chi_{7360}(3, \cdot)\) n/a 91840 80
7360.2.fa \(\chi_{7360}(53, \cdot)\) n/a 91840 80
7360.2.fd \(\chi_{7360}(11, \cdot)\) n/a 61440 80
7360.2.fe \(\chi_{7360}(19, \cdot)\) n/a 91840 80
7360.2.fh \(\chi_{7360}(29, \cdot)\) n/a 91840 80
7360.2.fi \(\chi_{7360}(101, \cdot)\) n/a 61440 80
7360.2.fl \(\chi_{7360}(123, \cdot)\) n/a 91840 80
7360.2.fn \(\chi_{7360}(37, \cdot)\) n/a 91840 80

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

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_1(7360))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_1(7360)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_1(16))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(20))\)\(^{\oplus 10}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(23))\)\(^{\oplus 14}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(32))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(40))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(46))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(64))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(80))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(92))\)\(^{\oplus 10}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(115))\)\(^{\oplus 7}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(160))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(184))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(230))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(320))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(368))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(460))\)\(^{\oplus 5}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(736))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(920))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(1472))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(1840))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(3680))\)\(^{\oplus 2}\)