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Properties

Label 9801.2
Level 9801
Weight 2
Dimension 2734084
Nonzero newspaces 32
Sturm bound 14113440

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Defining parameters

Level: \( N \) = \( 9801 = 3^{4} \cdot 11^{2} \)
Weight: \( k \) = \( 2 \)
Nonzero newspaces: \( 32 \)
Sturm bound: \(14113440\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_1(9801))\).

Total New Old
Modular forms 3545640 2749820 795820
Cusp forms 3511081 2734084 776997
Eisenstein series 34559 15736 18823

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_1(9801))\)

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
9801.2.a \(\chi_{9801}(1, \cdot)\) 9801.2.a.a 1 1
9801.2.a.b 1
9801.2.a.c 1
9801.2.a.d 1
9801.2.a.e 1
9801.2.a.f 1
9801.2.a.g 1
9801.2.a.h 1
9801.2.a.i 1
9801.2.a.j 1
9801.2.a.k 1
9801.2.a.l 1
9801.2.a.m 2
9801.2.a.n 2
9801.2.a.o 2
9801.2.a.p 2
9801.2.a.q 2
9801.2.a.r 2
9801.2.a.s 2
9801.2.a.t 2
9801.2.a.u 2
9801.2.a.v 2
9801.2.a.w 2
9801.2.a.x 2
9801.2.a.y 2
9801.2.a.z 2
9801.2.a.ba 2
9801.2.a.bb 2
9801.2.a.bc 2
9801.2.a.bd 3
9801.2.a.be 3
9801.2.a.bf 3
9801.2.a.bg 3
9801.2.a.bh 4
9801.2.a.bi 4
9801.2.a.bj 4
9801.2.a.bk 4
9801.2.a.bl 4
9801.2.a.bm 4
9801.2.a.bn 5
9801.2.a.bo 5
9801.2.a.bp 5
9801.2.a.bq 5
9801.2.a.br 6
9801.2.a.bs 6
9801.2.a.bt 6
9801.2.a.bu 6
9801.2.a.bv 8
9801.2.a.bw 8
9801.2.a.bx 8
9801.2.a.by 8
9801.2.a.bz 8
9801.2.a.ca 8
9801.2.a.cb 10
9801.2.a.cc 10
9801.2.a.cd 10
9801.2.a.ce 10
9801.2.a.cf 12
9801.2.a.cg 12
9801.2.a.ch 12
9801.2.a.ci 12
9801.2.a.cj 12
9801.2.a.ck 12
9801.2.a.cl 12
9801.2.a.cm 18
9801.2.a.cn 18
9801.2.a.co 18
9801.2.a.cp 18
9801.2.a.cq 24
9801.2.a.cr 24
9801.2.d \(\chi_{9801}(9800, \cdot)\) n/a 416 1
9801.2.e \(\chi_{9801}(3268, \cdot)\) n/a 854 2
9801.2.f \(\chi_{9801}(487, \cdot)\) n/a 1664 4
9801.2.g \(\chi_{9801}(3266, \cdot)\) n/a 848 2
9801.2.j \(\chi_{9801}(1090, \cdot)\) n/a 1908 6
9801.2.k \(\chi_{9801}(161, \cdot)\) n/a 1664 4
9801.2.n \(\chi_{9801}(892, \cdot)\) n/a 5240 10
9801.2.o \(\chi_{9801}(3052, \cdot)\) n/a 3392 8
9801.2.p \(\chi_{9801}(1088, \cdot)\) n/a 1896 6
9801.2.s \(\chi_{9801}(890, \cdot)\) n/a 5240 10
9801.2.v \(\chi_{9801}(364, \cdot)\) n/a 17496 18
9801.2.y \(\chi_{9801}(215, \cdot)\) n/a 3392 8
9801.2.z \(\chi_{9801}(298, \cdot)\) n/a 10520 20
9801.2.ba \(\chi_{9801}(856, \cdot)\) n/a 7584 24
9801.2.bd \(\chi_{9801}(362, \cdot)\) n/a 17352 18
9801.2.be \(\chi_{9801}(82, \cdot)\) n/a 20960 40
9801.2.bh \(\chi_{9801}(296, \cdot)\) n/a 10520 20
9801.2.bk \(\chi_{9801}(233, \cdot)\) n/a 7584 24
9801.2.bl \(\chi_{9801}(100, \cdot)\) n/a 23640 60
9801.2.bo \(\chi_{9801}(404, \cdot)\) n/a 20960 40
9801.2.bp \(\chi_{9801}(124, \cdot)\) n/a 69408 72
9801.2.bq \(\chi_{9801}(136, \cdot)\) n/a 42080 80
9801.2.bt \(\chi_{9801}(98, \cdot)\) n/a 23640 60
9801.2.bu \(\chi_{9801}(239, \cdot)\) n/a 69408 72
9801.2.bx \(\chi_{9801}(34, \cdot)\) n/a 213480 180
9801.2.by \(\chi_{9801}(107, \cdot)\) n/a 42080 80
9801.2.cb \(\chi_{9801}(37, \cdot)\) n/a 94560 240
9801.2.cc \(\chi_{9801}(32, \cdot)\) n/a 213480 180
9801.2.cf \(\chi_{9801}(8, \cdot)\) n/a 94560 240
9801.2.ci \(\chi_{9801}(4, \cdot)\) n/a 853920 720
9801.2.cl \(\chi_{9801}(2, \cdot)\) n/a 853920 720

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

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_1(9801))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_1(9801)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_1(1))\)\(^{\oplus 15}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(3))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(9))\)\(^{\oplus 9}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(11))\)\(^{\oplus 10}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(27))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(33))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(81))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(99))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(121))\)\(^{\oplus 5}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(297))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(363))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(891))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(1089))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(3267))\)\(^{\oplus 2}\)