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Properties

Label 4998.2
Level 4998
Weight 2
Dimension 161378
Nonzero newspaces 40
Sturm bound 2709504

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Defining parameters

Level: \( N \) = \( 4998 = 2 \cdot 3 \cdot 7^{2} \cdot 17 \)
Weight: \( k \) = \( 2 \)
Nonzero newspaces: \( 40 \)
Sturm bound: \(2709504\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_1(4998))\).

Total New Old
Modular forms 685056 161378 523678
Cusp forms 669697 161378 508319
Eisenstein series 15359 0 15359

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_1(4998))\)

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
4998.2.a \(\chi_{4998}(1, \cdot)\) 4998.2.a.a 1 1
4998.2.a.b 1
4998.2.a.c 1
4998.2.a.d 1
4998.2.a.e 1
4998.2.a.f 1
4998.2.a.g 1
4998.2.a.h 1
4998.2.a.i 1
4998.2.a.j 1
4998.2.a.k 1
4998.2.a.l 1
4998.2.a.m 1
4998.2.a.n 1
4998.2.a.o 1
4998.2.a.p 1
4998.2.a.q 1
4998.2.a.r 1
4998.2.a.s 1
4998.2.a.t 1
4998.2.a.u 1
4998.2.a.v 1
4998.2.a.w 1
4998.2.a.x 1
4998.2.a.y 1
4998.2.a.z 1
4998.2.a.ba 1
4998.2.a.bb 1
4998.2.a.bc 1
4998.2.a.bd 1
4998.2.a.be 1
4998.2.a.bf 1
4998.2.a.bg 1
4998.2.a.bh 1
4998.2.a.bi 1
4998.2.a.bj 1
4998.2.a.bk 1
4998.2.a.bl 1
4998.2.a.bm 1
4998.2.a.bn 1
4998.2.a.bo 1
4998.2.a.bp 1
4998.2.a.bq 1
4998.2.a.br 1
4998.2.a.bs 2
4998.2.a.bt 2
4998.2.a.bu 2
4998.2.a.bv 2
4998.2.a.bw 2
4998.2.a.bx 2
4998.2.a.by 2
4998.2.a.bz 2
4998.2.a.ca 2
4998.2.a.cb 2
4998.2.a.cc 2
4998.2.a.cd 2
4998.2.a.ce 2
4998.2.a.cf 2
4998.2.a.cg 3
4998.2.a.ch 3
4998.2.a.ci 3
4998.2.a.cj 3
4998.2.a.ck 4
4998.2.a.cl 4
4998.2.a.cm 4
4998.2.a.cn 4
4998.2.a.co 4
4998.2.a.cp 4
4998.2.b \(\chi_{4998}(883, \cdot)\) n/a 122 1
4998.2.e \(\chi_{4998}(4997, \cdot)\) n/a 240 1
4998.2.f \(\chi_{4998}(4115, \cdot)\) n/a 216 1
4998.2.i \(\chi_{4998}(4183, \cdot)\) n/a 216 2
4998.2.k \(\chi_{4998}(293, \cdot)\) n/a 480 2
4998.2.m \(\chi_{4998}(1177, \cdot)\) n/a 244 2
4998.2.p \(\chi_{4998}(4625, \cdot)\) n/a 424 2
4998.2.q \(\chi_{4998}(509, \cdot)\) n/a 480 2
4998.2.t \(\chi_{4998}(67, \cdot)\) n/a 240 2
4998.2.u \(\chi_{4998}(715, \cdot)\) n/a 912 6
4998.2.v \(\chi_{4998}(1471, \cdot)\) n/a 496 4
4998.2.x \(\chi_{4998}(587, \cdot)\) n/a 960 4
4998.2.z \(\chi_{4998}(803, \cdot)\) n/a 960 4
4998.2.bb \(\chi_{4998}(361, \cdot)\) n/a 480 4
4998.2.be \(\chi_{4998}(545, \cdot)\) n/a 1776 6
4998.2.bh \(\chi_{4998}(713, \cdot)\) n/a 2016 6
4998.2.bi \(\chi_{4998}(169, \cdot)\) n/a 1008 6
4998.2.bm \(\chi_{4998}(97, \cdot)\) n/a 960 8
4998.2.bn \(\chi_{4998}(197, \cdot)\) n/a 1968 8
4998.2.bo \(\chi_{4998}(205, \cdot)\) n/a 1776 12
4998.2.bq \(\chi_{4998}(655, \cdot)\) n/a 960 8
4998.2.bs \(\chi_{4998}(1097, \cdot)\) n/a 1920 8
4998.2.bt \(\chi_{4998}(421, \cdot)\) n/a 2016 12
4998.2.bv \(\chi_{4998}(251, \cdot)\) n/a 4032 12
4998.2.by \(\chi_{4998}(781, \cdot)\) n/a 2016 12
4998.2.bz \(\chi_{4998}(101, \cdot)\) n/a 4032 12
4998.2.cc \(\chi_{4998}(341, \cdot)\) n/a 3600 12
4998.2.ce \(\chi_{4998}(275, \cdot)\) n/a 3840 16
4998.2.cf \(\chi_{4998}(31, \cdot)\) n/a 1920 16
4998.2.cj \(\chi_{4998}(83, \cdot)\) n/a 8064 24
4998.2.cl \(\chi_{4998}(43, \cdot)\) n/a 4032 24
4998.2.cn \(\chi_{4998}(319, \cdot)\) n/a 4032 24
4998.2.cp \(\chi_{4998}(47, \cdot)\) n/a 8064 24
4998.2.cq \(\chi_{4998}(29, \cdot)\) n/a 16128 48
4998.2.cr \(\chi_{4998}(139, \cdot)\) n/a 8064 48
4998.2.cu \(\chi_{4998}(59, \cdot)\) n/a 16128 48
4998.2.cw \(\chi_{4998}(25, \cdot)\) n/a 8064 48
4998.2.da \(\chi_{4998}(61, \cdot)\) n/a 16128 96
4998.2.db \(\chi_{4998}(11, \cdot)\) n/a 32256 96

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

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_1(4998))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_1(4998)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_1(14))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(17))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(21))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(34))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(42))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(49))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(51))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(98))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(102))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(119))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(147))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(238))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(294))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(357))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(714))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(833))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(1666))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(2499))\)\(^{\oplus 2}\)