Properties

Label 6171.2
Level 6171
Weight 2
Dimension 1016874
Nonzero newspaces 40
Sturm bound 5575680

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Defining parameters

Level: \( N \) = \( 6171 = 3 \cdot 11^{2} \cdot 17 \)
Weight: \( k \) = \( 2 \)
Nonzero newspaces: \( 40 \)
Sturm bound: \(5575680\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_1(6171))\).

Total New Old
Modular forms 1404160 1025306 378854
Cusp forms 1383681 1016874 366807
Eisenstein series 20479 8432 12047

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_1(6171))\)

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
6171.2.a \(\chi_{6171}(1, \cdot)\) 6171.2.a.a 1 1
6171.2.a.b 1
6171.2.a.c 1
6171.2.a.d 1
6171.2.a.e 1
6171.2.a.f 1
6171.2.a.g 1
6171.2.a.h 1
6171.2.a.i 1
6171.2.a.j 2
6171.2.a.k 2
6171.2.a.l 2
6171.2.a.m 2
6171.2.a.n 2
6171.2.a.o 2
6171.2.a.p 2
6171.2.a.q 3
6171.2.a.r 3
6171.2.a.s 3
6171.2.a.t 4
6171.2.a.u 5
6171.2.a.v 5
6171.2.a.w 6
6171.2.a.x 6
6171.2.a.y 6
6171.2.a.z 6
6171.2.a.ba 6
6171.2.a.bb 6
6171.2.a.bc 6
6171.2.a.bd 7
6171.2.a.be 7
6171.2.a.bf 8
6171.2.a.bg 8
6171.2.a.bh 8
6171.2.a.bi 8
6171.2.a.bj 12
6171.2.a.bk 12
6171.2.a.bl 12
6171.2.a.bm 12
6171.2.a.bn 14
6171.2.a.bo 14
6171.2.a.bp 20
6171.2.a.bq 20
6171.2.a.br 20
6171.2.a.bs 20
6171.2.f \(\chi_{6171}(2177, \cdot)\) n/a 576 1
6171.2.g \(\chi_{6171}(3994, \cdot)\) n/a 328 1
6171.2.h \(\chi_{6171}(6170, \cdot)\) n/a 632 1
6171.2.i \(\chi_{6171}(2903, \cdot)\) n/a 1264 2
6171.2.j \(\chi_{6171}(727, \cdot)\) n/a 656 2
6171.2.m \(\chi_{6171}(511, \cdot)\) n/a 1152 4
6171.2.o \(\chi_{6171}(1090, \cdot)\) n/a 1304 4
6171.2.q \(\chi_{6171}(3266, \cdot)\) n/a 2528 4
6171.2.r \(\chi_{6171}(2702, \cdot)\) n/a 2528 4
6171.2.s \(\chi_{6171}(1291, \cdot)\) n/a 1296 4
6171.2.t \(\chi_{6171}(239, \cdot)\) n/a 2304 4
6171.2.y \(\chi_{6171}(562, \cdot)\) n/a 3520 10
6171.2.z \(\chi_{6171}(241, \cdot)\) n/a 2592 8
6171.2.ba \(\chi_{6171}(122, \cdot)\) n/a 5088 8
6171.2.bf \(\chi_{6171}(565, \cdot)\) n/a 2592 8
6171.2.bg \(\chi_{6171}(965, \cdot)\) n/a 5056 8
6171.2.bh \(\chi_{6171}(560, \cdot)\) n/a 7880 10
6171.2.bi \(\chi_{6171}(67, \cdot)\) n/a 3960 10
6171.2.bj \(\chi_{6171}(494, \cdot)\) n/a 7040 10
6171.2.bo \(\chi_{6171}(161, \cdot)\) n/a 10112 16
6171.2.bq \(\chi_{6171}(202, \cdot)\) n/a 5184 16
6171.2.bu \(\chi_{6171}(166, \cdot)\) n/a 7920 20
6171.2.bv \(\chi_{6171}(98, \cdot)\) n/a 15760 20
6171.2.bw \(\chi_{6171}(103, \cdot)\) n/a 14080 40
6171.2.bz \(\chi_{6171}(245, \cdot)\) n/a 20224 32
6171.2.ca \(\chi_{6171}(40, \cdot)\) n/a 10368 32
6171.2.cb \(\chi_{6171}(32, \cdot)\) n/a 31520 40
6171.2.cd \(\chi_{6171}(100, \cdot)\) n/a 15840 40
6171.2.cj \(\chi_{6171}(35, \cdot)\) n/a 28160 40
6171.2.ck \(\chi_{6171}(16, \cdot)\) n/a 15840 40
6171.2.cl \(\chi_{6171}(50, \cdot)\) n/a 31520 40
6171.2.co \(\chi_{6171}(23, \cdot)\) n/a 63040 80
6171.2.cp \(\chi_{6171}(10, \cdot)\) n/a 31680 80
6171.2.cq \(\chi_{6171}(140, \cdot)\) n/a 63040 80
6171.2.cr \(\chi_{6171}(4, \cdot)\) n/a 31680 80
6171.2.cv \(\chi_{6171}(25, \cdot)\) n/a 63360 160
6171.2.cx \(\chi_{6171}(2, \cdot)\) n/a 126080 160
6171.2.cy \(\chi_{6171}(7, \cdot)\) n/a 126720 320
6171.2.cz \(\chi_{6171}(5, \cdot)\) n/a 252160 320

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

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_1(6171))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_1(6171)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_1(11))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(17))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(33))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(51))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(121))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(187))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(363))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(561))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(2057))\)\(^{\oplus 2}\)