Properties

Label 6498.2
Level 6498
Weight 2
Dimension 306947
Nonzero newspaces 32
Sturm bound 4678560

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Defining parameters

Level: \( N \) = \( 6498 = 2 \cdot 3^{2} \cdot 19^{2} \)
Weight: \( k \) = \( 2 \)
Nonzero newspaces: \( 32 \)
Sturm bound: \(4678560\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_1(6498))\).

Total New Old
Modular forms 1177704 306947 870757
Cusp forms 1161577 306947 854630
Eisenstein series 16127 0 16127

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_1(6498))\)

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
6498.2.a \(\chi_{6498}(1, \cdot)\) 6498.2.a.a 1 1
6498.2.a.b 1
6498.2.a.c 1
6498.2.a.d 1
6498.2.a.e 1
6498.2.a.f 1
6498.2.a.g 1
6498.2.a.h 1
6498.2.a.i 1
6498.2.a.j 1
6498.2.a.k 1
6498.2.a.l 1
6498.2.a.m 1
6498.2.a.n 1
6498.2.a.o 1
6498.2.a.p 1
6498.2.a.q 1
6498.2.a.r 1
6498.2.a.s 1
6498.2.a.t 1
6498.2.a.u 1
6498.2.a.v 1
6498.2.a.w 1
6498.2.a.x 1
6498.2.a.y 1
6498.2.a.z 2
6498.2.a.ba 2
6498.2.a.bb 2
6498.2.a.bc 2
6498.2.a.bd 2
6498.2.a.be 2
6498.2.a.bf 2
6498.2.a.bg 2
6498.2.a.bh 2
6498.2.a.bi 2
6498.2.a.bj 2
6498.2.a.bk 2
6498.2.a.bl 3
6498.2.a.bm 3
6498.2.a.bn 3
6498.2.a.bo 3
6498.2.a.bp 3
6498.2.a.bq 3
6498.2.a.br 3
6498.2.a.bs 3
6498.2.a.bt 3
6498.2.a.bu 3
6498.2.a.bv 4
6498.2.a.bw 4
6498.2.a.bx 4
6498.2.a.by 4
6498.2.a.bz 4
6498.2.a.ca 4
6498.2.a.cb 6
6498.2.a.cc 6
6498.2.a.cd 6
6498.2.a.ce 6
6498.2.a.cf 8
6498.2.a.cg 8
6498.2.b \(\chi_{6498}(6497, \cdot)\) n/a 116 1
6498.2.e \(\chi_{6498}(2167, \cdot)\) n/a 682 2
6498.2.f \(\chi_{6498}(1375, \cdot)\) n/a 680 2
6498.2.g \(\chi_{6498}(1873, \cdot)\) n/a 286 2
6498.2.h \(\chi_{6498}(3541, \cdot)\) n/a 680 2
6498.2.j \(\chi_{6498}(2459, \cdot)\) n/a 680 2
6498.2.n \(\chi_{6498}(293, \cdot)\) n/a 680 2
6498.2.p \(\chi_{6498}(2165, \cdot)\) n/a 680 2
6498.2.s \(\chi_{6498}(791, \cdot)\) n/a 232 2
6498.2.u \(\chi_{6498}(415, \cdot)\) n/a 846 6
6498.2.v \(\chi_{6498}(967, \cdot)\) n/a 2040 6
6498.2.w \(\chi_{6498}(1111, \cdot)\) n/a 2040 6
6498.2.x \(\chi_{6498}(623, \cdot)\) n/a 2040 6
6498.2.bb \(\chi_{6498}(2465, \cdot)\) n/a 672 6
6498.2.bf \(\chi_{6498}(299, \cdot)\) n/a 2040 6
6498.2.bg \(\chi_{6498}(343, \cdot)\) n/a 2826 18
6498.2.bj \(\chi_{6498}(341, \cdot)\) n/a 2232 18
6498.2.bk \(\chi_{6498}(121, \cdot)\) n/a 13680 36
6498.2.bl \(\chi_{6498}(163, \cdot)\) n/a 5652 36
6498.2.bm \(\chi_{6498}(7, \cdot)\) n/a 13680 36
6498.2.bn \(\chi_{6498}(115, \cdot)\) n/a 13680 36
6498.2.bp \(\chi_{6498}(107, \cdot)\) n/a 4464 36
6498.2.bs \(\chi_{6498}(113, \cdot)\) n/a 13680 36
6498.2.bu \(\chi_{6498}(335, \cdot)\) n/a 13680 36
6498.2.by \(\chi_{6498}(65, \cdot)\) n/a 13680 36
6498.2.ca \(\chi_{6498}(43, \cdot)\) n/a 41040 108
6498.2.cb \(\chi_{6498}(25, \cdot)\) n/a 41040 108
6498.2.cc \(\chi_{6498}(55, \cdot)\) n/a 17172 108
6498.2.cd \(\chi_{6498}(155, \cdot)\) n/a 41040 108
6498.2.ch \(\chi_{6498}(53, \cdot)\) n/a 13824 108
6498.2.cl \(\chi_{6498}(29, \cdot)\) n/a 41040 108

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

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_1(6498))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_1(6498)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_1(18))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(19))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(38))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(57))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(114))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(171))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(342))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(361))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(722))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(1083))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(2166))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(3249))\)\(^{\oplus 2}\)