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Properties

Label 5408.2
Level 5408
Weight 2
Dimension 502981
Nonzero newspaces 40
Sturm bound 3634176

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Defining parameters

Level: \( N \) = \( 5408 = 2^{5} \cdot 13^{2} \)
Weight: \( k \) = \( 2 \)
Nonzero newspaces: \( 40 \)
Sturm bound: \(3634176\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_1(5408))\).

Total New Old
Modular forms 915840 507071 408769
Cusp forms 901249 502981 398268
Eisenstein series 14591 4090 10501

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_1(5408))\)

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
5408.2.a \(\chi_{5408}(1, \cdot)\) 5408.2.a.a 1 1
5408.2.a.b 1
5408.2.a.c 1
5408.2.a.d 1
5408.2.a.e 1
5408.2.a.f 1
5408.2.a.g 1
5408.2.a.h 1
5408.2.a.i 1
5408.2.a.j 1
5408.2.a.k 1
5408.2.a.l 1
5408.2.a.m 1
5408.2.a.n 2
5408.2.a.o 2
5408.2.a.p 2
5408.2.a.q 2
5408.2.a.r 2
5408.2.a.s 2
5408.2.a.t 2
5408.2.a.u 2
5408.2.a.v 2
5408.2.a.w 2
5408.2.a.x 2
5408.2.a.y 2
5408.2.a.z 2
5408.2.a.ba 2
5408.2.a.bb 2
5408.2.a.bc 2
5408.2.a.bd 2
5408.2.a.be 2
5408.2.a.bf 2
5408.2.a.bg 4
5408.2.a.bh 4
5408.2.a.bi 4
5408.2.a.bj 4
5408.2.a.bk 4
5408.2.a.bl 6
5408.2.a.bm 6
5408.2.a.bn 6
5408.2.a.bo 6
5408.2.a.bp 9
5408.2.a.bq 9
5408.2.a.br 9
5408.2.a.bs 9
5408.2.a.bt 12
5408.2.a.bu 12
5408.2.b \(\chi_{5408}(2705, \cdot)\) n/a 144 1
5408.2.e \(\chi_{5408}(337, \cdot)\) n/a 144 1
5408.2.f \(\chi_{5408}(3041, \cdot)\) n/a 154 1
5408.2.i \(\chi_{5408}(3233, \cdot)\) n/a 308 2
5408.2.k \(\chi_{5408}(2943, \cdot)\) n/a 308 2
5408.2.l \(\chi_{5408}(775, \cdot)\) None 0 2
5408.2.n \(\chi_{5408}(1353, \cdot)\) None 0 2
5408.2.p \(\chi_{5408}(1689, \cdot)\) None 0 2
5408.2.s \(\chi_{5408}(3479, \cdot)\) None 0 2
5408.2.u \(\chi_{5408}(239, \cdot)\) n/a 288 2
5408.2.w \(\chi_{5408}(4417, \cdot)\) n/a 308 2
5408.2.z \(\chi_{5408}(529, \cdot)\) n/a 288 2
5408.2.ba \(\chi_{5408}(1713, \cdot)\) n/a 288 2
5408.2.bd \(\chi_{5408}(915, \cdot)\) n/a 2424 4
5408.2.bf \(\chi_{5408}(677, \cdot)\) n/a 2436 4
5408.2.bg \(\chi_{5408}(1013, \cdot)\) n/a 2424 4
5408.2.bi \(\chi_{5408}(99, \cdot)\) n/a 2424 4
5408.2.bk \(\chi_{5408}(1103, \cdot)\) n/a 576 4
5408.2.bn \(\chi_{5408}(695, \cdot)\) None 0 4
5408.2.bp \(\chi_{5408}(361, \cdot)\) None 0 4
5408.2.br \(\chi_{5408}(1881, \cdot)\) None 0 4
5408.2.bs \(\chi_{5408}(2455, \cdot)\) None 0 4
5408.2.bu \(\chi_{5408}(319, \cdot)\) n/a 616 4
5408.2.bw \(\chi_{5408}(417, \cdot)\) n/a 2184 12
5408.2.by \(\chi_{5408}(587, \cdot)\) n/a 4848 8
5408.2.ca \(\chi_{5408}(485, \cdot)\) n/a 4848 8
5408.2.cb \(\chi_{5408}(653, \cdot)\) n/a 4848 8
5408.2.cd \(\chi_{5408}(19, \cdot)\) n/a 4848 8
5408.2.ch \(\chi_{5408}(129, \cdot)\) n/a 2184 12
5408.2.ci \(\chi_{5408}(753, \cdot)\) n/a 2160 12
5408.2.cl \(\chi_{5408}(209, \cdot)\) n/a 2160 12
5408.2.cm \(\chi_{5408}(289, \cdot)\) n/a 4368 24
5408.2.co \(\chi_{5408}(47, \cdot)\) n/a 4320 24
5408.2.cp \(\chi_{5408}(135, \cdot)\) None 0 24
5408.2.cr \(\chi_{5408}(25, \cdot)\) None 0 24
5408.2.ct \(\chi_{5408}(105, \cdot)\) None 0 24
5408.2.cw \(\chi_{5408}(343, \cdot)\) None 0 24
5408.2.cy \(\chi_{5408}(31, \cdot)\) n/a 4368 24
5408.2.da \(\chi_{5408}(17, \cdot)\) n/a 4320 24
5408.2.db \(\chi_{5408}(81, \cdot)\) n/a 4320 24
5408.2.de \(\chi_{5408}(225, \cdot)\) n/a 4368 24
5408.2.dh \(\chi_{5408}(187, \cdot)\) n/a 34848 48
5408.2.dj \(\chi_{5408}(77, \cdot)\) n/a 34848 48
5408.2.dk \(\chi_{5408}(53, \cdot)\) n/a 34848 48
5408.2.dm \(\chi_{5408}(83, \cdot)\) n/a 34848 48
5408.2.do \(\chi_{5408}(63, \cdot)\) n/a 8736 48
5408.2.dr \(\chi_{5408}(71, \cdot)\) None 0 48
5408.2.dt \(\chi_{5408}(9, \cdot)\) None 0 48
5408.2.dv \(\chi_{5408}(121, \cdot)\) None 0 48
5408.2.dw \(\chi_{5408}(7, \cdot)\) None 0 48
5408.2.dy \(\chi_{5408}(15, \cdot)\) n/a 8640 48
5408.2.eb \(\chi_{5408}(11, \cdot)\) n/a 69696 96
5408.2.ed \(\chi_{5408}(29, \cdot)\) n/a 69696 96
5408.2.ee \(\chi_{5408}(69, \cdot)\) n/a 69696 96
5408.2.eg \(\chi_{5408}(115, \cdot)\) n/a 69696 96

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

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_1(5408))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_1(5408)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_1(1))\)\(^{\oplus 18}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(2))\)\(^{\oplus 15}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(4))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(8))\)\(^{\oplus 9}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(13))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(16))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(26))\)\(^{\oplus 10}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(32))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(52))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(104))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(169))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(208))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(338))\)\(^{\oplus 5}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(416))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(676))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(1352))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(2704))\)\(^{\oplus 2}\)