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Properties

Label 9898.2
Level 9898
Weight 2
Dimension 959035
Nonzero newspaces 36
Sturm bound 11995200

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Defining parameters

Level: \( N \) = \( 9898 = 2 \cdot 7^{2} \cdot 101 \)
Weight: \( k \) = \( 2 \)
Nonzero newspaces: \( 36 \)
Sturm bound: \(11995200\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_1(9898))\).

Total New Old
Modular forms 3010800 959035 2051765
Cusp forms 2986801 959035 2027766
Eisenstein series 23999 0 23999

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_1(9898))\)

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
9898.2.a \(\chi_{9898}(1, \cdot)\) 9898.2.a.a 1 1
9898.2.a.b 1
9898.2.a.c 1
9898.2.a.d 1
9898.2.a.e 1
9898.2.a.f 1
9898.2.a.g 1
9898.2.a.h 1
9898.2.a.i 1
9898.2.a.j 1
9898.2.a.k 2
9898.2.a.l 2
9898.2.a.m 2
9898.2.a.n 2
9898.2.a.o 3
9898.2.a.p 4
9898.2.a.q 4
9898.2.a.r 4
9898.2.a.s 4
9898.2.a.t 5
9898.2.a.u 7
9898.2.a.v 7
9898.2.a.w 8
9898.2.a.x 9
9898.2.a.y 11
9898.2.a.z 11
9898.2.a.ba 12
9898.2.a.bb 12
9898.2.a.bc 12
9898.2.a.bd 12
9898.2.a.be 13
9898.2.a.bf 13
9898.2.a.bg 19
9898.2.a.bh 19
9898.2.a.bi 20
9898.2.a.bj 20
9898.2.a.bk 24
9898.2.a.bl 24
9898.2.a.bm 24
9898.2.a.bn 24
9898.2.c \(\chi_{9898}(6665, \cdot)\) n/a 348 1
9898.2.e \(\chi_{9898}(2223, \cdot)\) n/a 664 2
9898.2.f \(\chi_{9898}(293, \cdot)\) n/a 680 2
9898.2.h \(\chi_{9898}(491, \cdot)\) n/a 1396 4
9898.2.j \(\chi_{9898}(8887, \cdot)\) n/a 680 2
9898.2.l \(\chi_{9898}(1415, \cdot)\) n/a 2784 6
9898.2.n \(\chi_{9898}(3137, \cdot)\) n/a 1392 4
9898.2.q \(\chi_{9898}(313, \cdot)\) n/a 1360 4
9898.2.s \(\chi_{9898}(1009, \cdot)\) n/a 2856 6
9898.2.u \(\chi_{9898}(2713, \cdot)\) n/a 2720 8
9898.2.w \(\chi_{9898}(4311, \cdot)\) n/a 2720 8
9898.2.x \(\chi_{9898}(809, \cdot)\) n/a 5616 12
9898.2.y \(\chi_{9898}(687, \cdot)\) n/a 6980 20
9898.2.ba \(\chi_{9898}(111, \cdot)\) n/a 5712 12
9898.2.bc \(\chi_{9898}(5359, \cdot)\) n/a 2720 8
9898.2.be \(\chi_{9898}(701, \cdot)\) n/a 11424 24
9898.2.bg \(\chi_{9898}(403, \cdot)\) n/a 5712 12
9898.2.bi \(\chi_{9898}(197, \cdot)\) n/a 6960 20
9898.2.bl \(\chi_{9898}(1685, \cdot)\) n/a 5440 16
9898.2.bo \(\chi_{9898}(267, \cdot)\) n/a 11424 24
9898.2.bq \(\chi_{9898}(79, \cdot)\) n/a 13600 40
9898.2.br \(\chi_{9898}(495, \cdot)\) n/a 11424 24
9898.2.bt \(\chi_{9898}(195, \cdot)\) n/a 13600 40
9898.2.bv \(\chi_{9898}(95, \cdot)\) n/a 22848 48
9898.2.bw \(\chi_{9898}(41, \cdot)\) n/a 22848 48
9898.2.ca \(\chi_{9898}(165, \cdot)\) n/a 13600 40
9898.2.cb \(\chi_{9898}(71, \cdot)\) n/a 57120 120
9898.2.cd \(\chi_{9898}(65, \cdot)\) n/a 22848 48
9898.2.cg \(\chi_{9898}(129, \cdot)\) n/a 27200 80
9898.2.cj \(\chi_{9898}(43, \cdot)\) n/a 57120 120
9898.2.cl \(\chi_{9898}(145, \cdot)\) n/a 45696 96
9898.2.cm \(\chi_{9898}(25, \cdot)\) n/a 114240 240
9898.2.co \(\chi_{9898}(27, \cdot)\) n/a 114240 240
9898.2.cp \(\chi_{9898}(9, \cdot)\) n/a 114240 240
9898.2.cs \(\chi_{9898}(3, \cdot)\) n/a 228480 480

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

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_1(9898))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_1(9898)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_1(1))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(2))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(7))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(14))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(49))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(98))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(101))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(202))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(707))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(1414))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(4949))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(9898))\)\(^{\oplus 1}\)