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Properties

Label 5929.2
Level 5929
Weight 2
Dimension 1336194
Nonzero newspaces 32
Sturm bound 5691840

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Defining parameters

Level: \( N \) = \( 5929 = 7^{2} \cdot 11^{2} \)
Weight: \( k \) = \( 2 \)
Nonzero newspaces: \( 32 \)
Sturm bound: \(5691840\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_1(5929))\).

Total New Old
Modular forms 1432560 1349823 82737
Cusp forms 1413361 1336194 77167
Eisenstein series 19199 13629 5570

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_1(5929))\)

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
5929.2.a \(\chi_{5929}(1, \cdot)\) 5929.2.a.a 1 1
5929.2.a.b 1
5929.2.a.c 1
5929.2.a.d 1
5929.2.a.e 1
5929.2.a.f 1
5929.2.a.g 1
5929.2.a.h 1
5929.2.a.i 2
5929.2.a.j 2
5929.2.a.k 2
5929.2.a.l 2
5929.2.a.m 2
5929.2.a.n 2
5929.2.a.o 2
5929.2.a.p 2
5929.2.a.q 2
5929.2.a.r 2
5929.2.a.s 2
5929.2.a.t 3
5929.2.a.u 3
5929.2.a.v 3
5929.2.a.w 3
5929.2.a.x 3
5929.2.a.y 3
5929.2.a.z 4
5929.2.a.ba 4
5929.2.a.bb 4
5929.2.a.bc 4
5929.2.a.bd 4
5929.2.a.be 4
5929.2.a.bf 4
5929.2.a.bg 4
5929.2.a.bh 4
5929.2.a.bi 4
5929.2.a.bj 6
5929.2.a.bk 6
5929.2.a.bl 6
5929.2.a.bm 6
5929.2.a.bn 7
5929.2.a.bo 7
5929.2.a.bp 7
5929.2.a.bq 7
5929.2.a.br 8
5929.2.a.bs 8
5929.2.a.bt 8
5929.2.a.bu 8
5929.2.a.bv 10
5929.2.a.bw 10
5929.2.a.bx 10
5929.2.a.by 10
5929.2.a.bz 10
5929.2.a.ca 12
5929.2.a.cb 12
5929.2.a.cc 12
5929.2.a.cd 14
5929.2.a.ce 14
5929.2.a.cf 16
5929.2.a.cg 24
5929.2.a.ch 24
5929.2.b \(\chi_{5929}(5928, \cdot)\) n/a 344 1
5929.2.e \(\chi_{5929}(606, \cdot)\) n/a 690 2
5929.2.f \(\chi_{5929}(148, \cdot)\) n/a 1396 4
5929.2.i \(\chi_{5929}(362, \cdot)\) n/a 688 2
5929.2.j \(\chi_{5929}(848, \cdot)\) n/a 2994 6
5929.2.m \(\chi_{5929}(1322, \cdot)\) n/a 1376 4
5929.2.n \(\chi_{5929}(540, \cdot)\) n/a 4460 10
5929.2.q \(\chi_{5929}(846, \cdot)\) n/a 2976 6
5929.2.r \(\chi_{5929}(753, \cdot)\) n/a 2752 8
5929.2.s \(\chi_{5929}(485, \cdot)\) n/a 6000 12
5929.2.u \(\chi_{5929}(538, \cdot)\) n/a 4360 10
5929.2.w \(\chi_{5929}(215, \cdot)\) n/a 2752 8
5929.2.z \(\chi_{5929}(67, \cdot)\) n/a 8720 20
5929.2.ba \(\chi_{5929}(323, \cdot)\) n/a 11904 24
5929.2.bb \(\chi_{5929}(241, \cdot)\) n/a 5952 12
5929.2.be \(\chi_{5929}(246, \cdot)\) n/a 17840 40
5929.2.bg \(\chi_{5929}(472, \cdot)\) n/a 8720 20
5929.2.bi \(\chi_{5929}(118, \cdot)\) n/a 11904 24
5929.2.bl \(\chi_{5929}(78, \cdot)\) n/a 36840 60
5929.2.bm \(\chi_{5929}(9, \cdot)\) n/a 23808 48
5929.2.bo \(\chi_{5929}(195, \cdot)\) n/a 17440 40
5929.2.br \(\chi_{5929}(76, \cdot)\) n/a 36840 60
5929.2.bt \(\chi_{5929}(214, \cdot)\) n/a 34880 80
5929.2.bw \(\chi_{5929}(40, \cdot)\) n/a 23808 48
5929.2.bx \(\chi_{5929}(23, \cdot)\) n/a 73680 120
5929.2.bz \(\chi_{5929}(19, \cdot)\) n/a 34880 80
5929.2.cb \(\chi_{5929}(15, \cdot)\) n/a 147360 240
5929.2.cd \(\chi_{5929}(10, \cdot)\) n/a 73680 120
5929.2.cg \(\chi_{5929}(6, \cdot)\) n/a 147360 240
5929.2.ci \(\chi_{5929}(4, \cdot)\) n/a 294720 480
5929.2.ck \(\chi_{5929}(17, \cdot)\) n/a 294720 480

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

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_1(5929))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_1(5929)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_1(11))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(49))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(77))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(121))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(539))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(847))\)\(^{\oplus 2}\)