Properties

Label 8036.2
Level 8036
Weight 2
Dimension 1100830
Nonzero newspaces 64
Sturm bound 7902720

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Defining parameters

Level: \( N \) = \( 8036 = 2^{2} \cdot 7^{2} \cdot 41 \)
Weight: \( k \) = \( 2 \)
Nonzero newspaces: \( 64 \)
Sturm bound: \(7902720\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_1(8036))\).

Total New Old
Modular forms 1987680 1108398 879282
Cusp forms 1963681 1100830 862851
Eisenstein series 23999 7568 16431

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_1(8036))\)

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
8036.2.a \(\chi_{8036}(1, \cdot)\) 8036.2.a.a 1 1
8036.2.a.b 1
8036.2.a.c 1
8036.2.a.d 1
8036.2.a.e 1
8036.2.a.f 1
8036.2.a.g 2
8036.2.a.h 3
8036.2.a.i 4
8036.2.a.j 5
8036.2.a.k 5
8036.2.a.l 5
8036.2.a.m 8
8036.2.a.n 8
8036.2.a.o 10
8036.2.a.p 10
8036.2.a.q 15
8036.2.a.r 15
8036.2.a.s 20
8036.2.a.t 20
8036.2.c \(\chi_{8036}(8035, \cdot)\) n/a 832 1
8036.2.d \(\chi_{8036}(4509, \cdot)\) n/a 144 1
8036.2.f \(\chi_{8036}(3527, \cdot)\) n/a 800 1
8036.2.i \(\chi_{8036}(165, \cdot)\) n/a 268 2
8036.2.k \(\chi_{8036}(6077, \cdot)\) n/a 286 2
8036.2.l \(\chi_{8036}(1567, \cdot)\) n/a 1664 2
8036.2.n \(\chi_{8036}(2353, \cdot)\) n/a 576 4
8036.2.p \(\chi_{8036}(411, \cdot)\) n/a 1600 2
8036.2.r \(\chi_{8036}(4673, \cdot)\) n/a 280 2
8036.2.u \(\chi_{8036}(4919, \cdot)\) n/a 1664 2
8036.2.v \(\chi_{8036}(1149, \cdot)\) n/a 1128 6
8036.2.x \(\chi_{8036}(489, \cdot)\) n/a 560 4
8036.2.z \(\chi_{8036}(1667, \cdot)\) n/a 3404 4
8036.2.bb \(\chi_{8036}(2157, \cdot)\) n/a 576 4
8036.2.bc \(\chi_{8036}(195, \cdot)\) n/a 3328 4
8036.2.bg \(\chi_{8036}(1371, \cdot)\) n/a 3328 4
8036.2.bi \(\chi_{8036}(1403, \cdot)\) n/a 3328 4
8036.2.bj \(\chi_{8036}(1157, \cdot)\) n/a 560 4
8036.2.bn \(\chi_{8036}(83, \cdot)\) n/a 6720 6
8036.2.bp \(\chi_{8036}(1065, \cdot)\) n/a 1176 6
8036.2.bq \(\chi_{8036}(1147, \cdot)\) n/a 7032 6
8036.2.bs \(\chi_{8036}(961, \cdot)\) n/a 1120 8
8036.2.bu \(\chi_{8036}(979, \cdot)\) n/a 6656 8
8036.2.bv \(\chi_{8036}(197, \cdot)\) n/a 1144 8
8036.2.bx \(\chi_{8036}(821, \cdot)\) n/a 2232 12
8036.2.by \(\chi_{8036}(79, \cdot)\) n/a 6656 8
8036.2.ca \(\chi_{8036}(325, \cdot)\) n/a 1120 8
8036.2.cd \(\chi_{8036}(419, \cdot)\) n/a 14064 12
8036.2.ce \(\chi_{8036}(337, \cdot)\) n/a 2352 12
8036.2.ch \(\chi_{8036}(215, \cdot)\) n/a 6656 8
8036.2.cj \(\chi_{8036}(31, \cdot)\) n/a 6656 8
8036.2.cm \(\chi_{8036}(373, \cdot)\) n/a 1120 8
8036.2.cn \(\chi_{8036}(57, \cdot)\) n/a 4704 24
8036.2.co \(\chi_{8036}(99, \cdot)\) n/a 13616 16
8036.2.cq \(\chi_{8036}(97, \cdot)\) n/a 2240 16
8036.2.cs \(\chi_{8036}(327, \cdot)\) n/a 14064 12
8036.2.cv \(\chi_{8036}(81, \cdot)\) n/a 2352 12
8036.2.cx \(\chi_{8036}(1067, \cdot)\) n/a 13440 12
8036.2.da \(\chi_{8036}(407, \cdot)\) n/a 28128 24
8036.2.dc \(\chi_{8036}(601, \cdot)\) n/a 4704 24
8036.2.de \(\chi_{8036}(361, \cdot)\) n/a 2240 16
8036.2.df \(\chi_{8036}(607, \cdot)\) n/a 13312 16
8036.2.dh \(\chi_{8036}(139, \cdot)\) n/a 28128 24
8036.2.dl \(\chi_{8036}(1007, \cdot)\) n/a 28128 24
8036.2.dm \(\chi_{8036}(113, \cdot)\) n/a 4704 24
8036.2.dp \(\chi_{8036}(9, \cdot)\) n/a 4704 24
8036.2.dq \(\chi_{8036}(255, \cdot)\) n/a 28128 24
8036.2.ds \(\chi_{8036}(37, \cdot)\) n/a 9408 48
8036.2.du \(\chi_{8036}(117, \cdot)\) n/a 4480 32
8036.2.dw \(\chi_{8036}(67, \cdot)\) n/a 26624 32
8036.2.dy \(\chi_{8036}(169, \cdot)\) n/a 9408 48
8036.2.dz \(\chi_{8036}(251, \cdot)\) n/a 56256 48
8036.2.eb \(\chi_{8036}(437, \cdot)\) n/a 9408 48
8036.2.ed \(\chi_{8036}(191, \cdot)\) n/a 56256 48
8036.2.ef \(\chi_{8036}(25, \cdot)\) n/a 9408 48
8036.2.ei \(\chi_{8036}(187, \cdot)\) n/a 56256 48
8036.2.ek \(\chi_{8036}(59, \cdot)\) n/a 56256 48
8036.2.em \(\chi_{8036}(13, \cdot)\) n/a 18816 96
8036.2.eo \(\chi_{8036}(15, \cdot)\) n/a 112512 96
8036.2.er \(\chi_{8036}(87, \cdot)\) n/a 112512 96
8036.2.es \(\chi_{8036}(121, \cdot)\) n/a 18816 96
8036.2.ev \(\chi_{8036}(11, \cdot)\) n/a 225024 192
8036.2.ex \(\chi_{8036}(17, \cdot)\) n/a 37632 192

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

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_1(8036))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_1(8036)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_1(14))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(28))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(41))\)\(^{\oplus 9}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(49))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(82))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(98))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(164))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(196))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(287))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(574))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(1148))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(2009))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(4018))\)\(^{\oplus 2}\)