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Properties

Label 8496.2
Level 8496
Weight 2
Dimension 889799
Nonzero newspaces 32
Sturm bound 8017920

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Defining parameters

Level: \( N \) = \( 8496 = 2^{4} \cdot 3^{2} \cdot 59 \)
Weight: \( k \) = \( 2 \)
Nonzero newspaces: \( 32 \)
Sturm bound: \(8017920\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_1(8496))\).

Total New Old
Modular forms 2017472 894415 1123057
Cusp forms 1991489 889799 1101690
Eisenstein series 25983 4616 21367

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_1(8496))\)

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
8496.2.a \(\chi_{8496}(1, \cdot)\) 8496.2.a.a 1 1
8496.2.a.b 1
8496.2.a.c 1
8496.2.a.d 1
8496.2.a.e 1
8496.2.a.f 1
8496.2.a.g 1
8496.2.a.h 1
8496.2.a.i 1
8496.2.a.j 1
8496.2.a.k 1
8496.2.a.l 1
8496.2.a.m 1
8496.2.a.n 1
8496.2.a.o 1
8496.2.a.p 1
8496.2.a.q 1
8496.2.a.r 1
8496.2.a.s 1
8496.2.a.t 1
8496.2.a.u 1
8496.2.a.v 1
8496.2.a.w 1
8496.2.a.x 1
8496.2.a.y 2
8496.2.a.z 2
8496.2.a.ba 2
8496.2.a.bb 2
8496.2.a.bc 2
8496.2.a.bd 2
8496.2.a.be 2
8496.2.a.bf 2
8496.2.a.bg 2
8496.2.a.bh 3
8496.2.a.bi 3
8496.2.a.bj 3
8496.2.a.bk 3
8496.2.a.bl 3
8496.2.a.bm 3
8496.2.a.bn 3
8496.2.a.bo 4
8496.2.a.bp 4
8496.2.a.bq 4
8496.2.a.br 4
8496.2.a.bs 4
8496.2.a.bt 4
8496.2.a.bu 5
8496.2.a.bv 5
8496.2.a.bw 5
8496.2.a.bx 5
8496.2.a.by 5
8496.2.a.bz 5
8496.2.a.ca 6
8496.2.a.cb 6
8496.2.a.cc 8
8496.2.a.cd 8
8496.2.c \(\chi_{8496}(2359, \cdot)\) None 0 1
8496.2.e \(\chi_{8496}(7199, \cdot)\) n/a 116 1
8496.2.f \(\chi_{8496}(4249, \cdot)\) None 0 1
8496.2.h \(\chi_{8496}(3185, \cdot)\) n/a 120 1
8496.2.j \(\chi_{8496}(2951, \cdot)\) None 0 1
8496.2.l \(\chi_{8496}(6607, \cdot)\) n/a 150 1
8496.2.o \(\chi_{8496}(7433, \cdot)\) None 0 1
8496.2.q \(\chi_{8496}(2833, \cdot)\) n/a 696 2
8496.2.r \(\chi_{8496}(1061, \cdot)\) n/a 960 2
8496.2.t \(\chi_{8496}(2125, \cdot)\) n/a 1160 2
8496.2.v \(\chi_{8496}(827, \cdot)\) n/a 928 2
8496.2.x \(\chi_{8496}(235, \cdot)\) n/a 1196 2
8496.2.ba \(\chi_{8496}(1769, \cdot)\) None 0 2
8496.2.bd \(\chi_{8496}(943, \cdot)\) n/a 720 2
8496.2.bf \(\chi_{8496}(119, \cdot)\) None 0 2
8496.2.bh \(\chi_{8496}(353, \cdot)\) n/a 716 2
8496.2.bj \(\chi_{8496}(1417, \cdot)\) None 0 2
8496.2.bk \(\chi_{8496}(1535, \cdot)\) n/a 696 2
8496.2.bm \(\chi_{8496}(5191, \cdot)\) None 0 2
8496.2.bp \(\chi_{8496}(2243, \cdot)\) n/a 5568 4
8496.2.br \(\chi_{8496}(1651, \cdot)\) n/a 5744 4
8496.2.bt \(\chi_{8496}(2477, \cdot)\) n/a 5744 4
8496.2.bv \(\chi_{8496}(709, \cdot)\) n/a 5568 4
8496.2.bw \(\chi_{8496}(145, \cdot)\) n/a 4172 28
8496.2.by \(\chi_{8496}(89, \cdot)\) None 0 28
8496.2.cb \(\chi_{8496}(415, \cdot)\) n/a 4200 28
8496.2.cd \(\chi_{8496}(71, \cdot)\) None 0 28
8496.2.cf \(\chi_{8496}(161, \cdot)\) n/a 3360 28
8496.2.ch \(\chi_{8496}(361, \cdot)\) None 0 28
8496.2.ci \(\chi_{8496}(143, \cdot)\) n/a 3360 28
8496.2.ck \(\chi_{8496}(55, \cdot)\) None 0 28
8496.2.cm \(\chi_{8496}(49, \cdot)\) n/a 20048 56
8496.2.co \(\chi_{8496}(91, \cdot)\) n/a 33488 56
8496.2.cq \(\chi_{8496}(35, \cdot)\) n/a 26880 56
8496.2.cs \(\chi_{8496}(181, \cdot)\) n/a 33488 56
8496.2.cu \(\chi_{8496}(269, \cdot)\) n/a 26880 56
8496.2.cw \(\chi_{8496}(103, \cdot)\) None 0 56
8496.2.cy \(\chi_{8496}(95, \cdot)\) n/a 20160 56
8496.2.cz \(\chi_{8496}(25, \cdot)\) None 0 56
8496.2.db \(\chi_{8496}(65, \cdot)\) n/a 20048 56
8496.2.dd \(\chi_{8496}(167, \cdot)\) None 0 56
8496.2.df \(\chi_{8496}(31, \cdot)\) n/a 20160 56
8496.2.di \(\chi_{8496}(185, \cdot)\) None 0 56
8496.2.dk \(\chi_{8496}(85, \cdot)\) n/a 160832 112
8496.2.dm \(\chi_{8496}(77, \cdot)\) n/a 160832 112
8496.2.do \(\chi_{8496}(43, \cdot)\) n/a 160832 112
8496.2.dq \(\chi_{8496}(203, \cdot)\) n/a 160832 112

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

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_1(8496))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_1(8496)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_1(16))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(18))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(24))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(36))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(48))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(59))\)\(^{\oplus 15}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(72))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(118))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(144))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(177))\)\(^{\oplus 10}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(236))\)\(^{\oplus 9}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(354))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(472))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(531))\)\(^{\oplus 5}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(708))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(944))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(1062))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(1416))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(2124))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(2832))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(4248))\)\(^{\oplus 2}\)