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Properties

Label 7098.2
Level 7098
Weight 2
Dimension 322658
Nonzero newspaces 60
Sturm bound 5451264

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Defining parameters

Level: \( N \) = \( 7098 = 2 \cdot 3 \cdot 7 \cdot 13^{2} \)
Weight: \( k \) = \( 2 \)
Nonzero newspaces: \( 60 \)
Sturm bound: \(5451264\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_1(7098))\).

Total New Old
Modular forms 1373760 322658 1051102
Cusp forms 1351873 322658 1029215
Eisenstein series 21887 0 21887

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_1(7098))\)

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
7098.2.a \(\chi_{7098}(1, \cdot)\) 7098.2.a.a 1 1
7098.2.a.b 1
7098.2.a.c 1
7098.2.a.d 1
7098.2.a.e 1
7098.2.a.f 1
7098.2.a.g 1
7098.2.a.h 1
7098.2.a.i 1
7098.2.a.j 1
7098.2.a.k 1
7098.2.a.l 1
7098.2.a.m 1
7098.2.a.n 1
7098.2.a.o 1
7098.2.a.p 1
7098.2.a.q 1
7098.2.a.r 1
7098.2.a.s 1
7098.2.a.t 1
7098.2.a.u 1
7098.2.a.v 1
7098.2.a.w 1
7098.2.a.x 1
7098.2.a.y 1
7098.2.a.z 1
7098.2.a.ba 1
7098.2.a.bb 1
7098.2.a.bc 1
7098.2.a.bd 1
7098.2.a.be 1
7098.2.a.bf 1
7098.2.a.bg 2
7098.2.a.bh 2
7098.2.a.bi 2
7098.2.a.bj 2
7098.2.a.bk 2
7098.2.a.bl 2
7098.2.a.bm 2
7098.2.a.bn 2
7098.2.a.bo 2
7098.2.a.bp 2
7098.2.a.bq 2
7098.2.a.br 2
7098.2.a.bs 2
7098.2.a.bt 2
7098.2.a.bu 2
7098.2.a.bv 2
7098.2.a.bw 2
7098.2.a.bx 2
7098.2.a.by 2
7098.2.a.bz 2
7098.2.a.ca 2
7098.2.a.cb 3
7098.2.a.cc 3
7098.2.a.cd 3
7098.2.a.ce 3
7098.2.a.cf 3
7098.2.a.cg 3
7098.2.a.ch 3
7098.2.a.ci 3
7098.2.a.cj 3
7098.2.a.ck 3
7098.2.a.cl 3
7098.2.a.cm 3
7098.2.a.cn 4
7098.2.a.co 4
7098.2.a.cp 6
7098.2.a.cq 6
7098.2.a.cr 6
7098.2.a.cs 6
7098.2.a.ct 6
7098.2.a.cu 6
7098.2.c \(\chi_{7098}(337, \cdot)\) n/a 156 1
7098.2.e \(\chi_{7098}(7097, \cdot)\) n/a 408 1
7098.2.g \(\chi_{7098}(6761, \cdot)\) n/a 412 1
7098.2.i \(\chi_{7098}(4057, \cdot)\) n/a 412 2
7098.2.j \(\chi_{7098}(529, \cdot)\) n/a 412 2
7098.2.k \(\chi_{7098}(991, \cdot)\) n/a 412 2
7098.2.l \(\chi_{7098}(3571, \cdot)\) n/a 304 2
7098.2.o \(\chi_{7098}(4633, \cdot)\) n/a 416 2
7098.2.p \(\chi_{7098}(239, \cdot)\) n/a 616 2
7098.2.q \(\chi_{7098}(3065, \cdot)\) n/a 824 2
7098.2.s \(\chi_{7098}(3403, \cdot)\) n/a 312 2
7098.2.u \(\chi_{7098}(4247, \cdot)\) n/a 820 2
7098.2.z \(\chi_{7098}(677, \cdot)\) n/a 828 2
7098.2.bb \(\chi_{7098}(4709, \cdot)\) n/a 820 2
7098.2.bd \(\chi_{7098}(361, \cdot)\) n/a 412 2
7098.2.bg \(\chi_{7098}(1013, \cdot)\) n/a 824 2
7098.2.bi \(\chi_{7098}(4079, \cdot)\) n/a 820 2
7098.2.bk \(\chi_{7098}(4393, \cdot)\) n/a 408 2
7098.2.bm \(\chi_{7098}(823, \cdot)\) n/a 412 2
7098.2.bn \(\chi_{7098}(4541, \cdot)\) n/a 820 2
7098.2.bq \(\chi_{7098}(3233, \cdot)\) n/a 824 2
7098.2.bu \(\chi_{7098}(995, \cdot)\) n/a 1232 4
7098.2.bv \(\chi_{7098}(1451, \cdot)\) n/a 1648 4
7098.2.bw \(\chi_{7098}(695, \cdot)\) n/a 1640 4
7098.2.bx \(\chi_{7098}(1441, \cdot)\) n/a 816 4
7098.2.by \(\chi_{7098}(19, \cdot)\) n/a 824 4
7098.2.bz \(\chi_{7098}(577, \cdot)\) n/a 816 4
7098.2.cg \(\chi_{7098}(1333, \cdot)\) n/a 824 4
7098.2.ch \(\chi_{7098}(3131, \cdot)\) n/a 1640 4
7098.2.ci \(\chi_{7098}(547, \cdot)\) n/a 2208 12
7098.2.ck \(\chi_{7098}(209, \cdot)\) n/a 5856 12
7098.2.cm \(\chi_{7098}(545, \cdot)\) n/a 5856 12
7098.2.co \(\chi_{7098}(883, \cdot)\) n/a 2160 12
7098.2.cq \(\chi_{7098}(211, \cdot)\) n/a 4416 24
7098.2.cr \(\chi_{7098}(373, \cdot)\) n/a 5808 24
7098.2.cs \(\chi_{7098}(289, \cdot)\) n/a 5808 24
7098.2.ct \(\chi_{7098}(79, \cdot)\) n/a 5856 24
7098.2.cu \(\chi_{7098}(265, \cdot)\) n/a 5760 24
7098.2.cv \(\chi_{7098}(281, \cdot)\) n/a 8736 24
7098.2.cz \(\chi_{7098}(419, \cdot)\) n/a 11616 24
7098.2.dc \(\chi_{7098}(101, \cdot)\) n/a 11664 24
7098.2.dd \(\chi_{7098}(205, \cdot)\) n/a 5808 24
7098.2.df \(\chi_{7098}(25, \cdot)\) n/a 5856 24
7098.2.dh \(\chi_{7098}(17, \cdot)\) n/a 11664 24
7098.2.dj \(\chi_{7098}(311, \cdot)\) n/a 11616 24
7098.2.dm \(\chi_{7098}(121, \cdot)\) n/a 5808 24
7098.2.do \(\chi_{7098}(269, \cdot)\) n/a 11664 24
7098.2.dq \(\chi_{7098}(131, \cdot)\) n/a 11616 24
7098.2.dv \(\chi_{7098}(185, \cdot)\) n/a 11664 24
7098.2.dx \(\chi_{7098}(43, \cdot)\) n/a 4320 24
7098.2.dz \(\chi_{7098}(251, \cdot)\) n/a 11616 24
7098.2.ea \(\chi_{7098}(145, \cdot)\) n/a 11616 48
7098.2.eb \(\chi_{7098}(137, \cdot)\) n/a 23328 48
7098.2.ei \(\chi_{7098}(11, \cdot)\) n/a 23328 48
7098.2.ej \(\chi_{7098}(317, \cdot)\) n/a 23232 48
7098.2.ek \(\chi_{7098}(71, \cdot)\) n/a 17472 48
7098.2.el \(\chi_{7098}(31, \cdot)\) n/a 11712 48
7098.2.em \(\chi_{7098}(115, \cdot)\) n/a 11616 48
7098.2.en \(\chi_{7098}(97, \cdot)\) n/a 11712 48

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

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_1(7098))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_1(7098)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_1(1))\)\(^{\oplus 24}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(2))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(3))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(6))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(7))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(13))\)\(^{\oplus 16}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(14))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(21))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(26))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(39))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(42))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(78))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(91))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(169))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(182))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(273))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(338))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(507))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(546))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(1014))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(1183))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(2366))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(3549))\)\(^{\oplus 2}\)