Properties

Label 8046.2
Level 8046
Weight 2
Dimension 473556
Nonzero newspaces 18
Sturm bound 7192800

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Defining parameters

Level: \( N \) = \( 8046 = 2 \cdot 3^{3} \cdot 149 \)
Weight: \( k \) = \( 2 \)
Nonzero newspaces: \( 18 \)
Sturm bound: \(7192800\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_1(8046))\).

Total New Old
Modular forms 1807080 473556 1333524
Cusp forms 1789321 473556 1315765
Eisenstein series 17759 0 17759

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_1(8046))\)

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
8046.2.a \(\chi_{8046}(1, \cdot)\) 8046.2.a.a 1 1
8046.2.a.b 1
8046.2.a.c 2
8046.2.a.d 2
8046.2.a.e 8
8046.2.a.f 8
8046.2.a.g 9
8046.2.a.h 9
8046.2.a.i 12
8046.2.a.j 12
8046.2.a.k 12
8046.2.a.l 12
8046.2.a.m 12
8046.2.a.n 12
8046.2.a.o 12
8046.2.a.p 12
8046.2.a.q 14
8046.2.a.r 14
8046.2.a.s 16
8046.2.a.t 16
8046.2.d \(\chi_{8046}(595, \cdot)\) n/a 200 1
8046.2.e \(\chi_{8046}(2683, \cdot)\) n/a 296 2
8046.2.f \(\chi_{8046}(701, \cdot)\) n/a 400 2
8046.2.h \(\chi_{8046}(3277, \cdot)\) n/a 300 2
8046.2.k \(\chi_{8046}(895, \cdot)\) n/a 2664 6
8046.2.m \(\chi_{8046}(1385, \cdot)\) n/a 600 4
8046.2.n \(\chi_{8046}(1489, \cdot)\) n/a 2700 6
8046.2.r \(\chi_{8046}(491, \cdot)\) n/a 5400 12
8046.2.s \(\chi_{8046}(379, \cdot)\) n/a 7200 36
8046.2.t \(\chi_{8046}(217, \cdot)\) n/a 7200 36
8046.2.w \(\chi_{8046}(19, \cdot)\) n/a 10800 72
8046.2.y \(\chi_{8046}(161, \cdot)\) n/a 14400 72
8046.2.bb \(\chi_{8046}(235, \cdot)\) n/a 10800 72
8046.2.bc \(\chi_{8046}(25, \cdot)\) n/a 97200 216
8046.2.bd \(\chi_{8046}(71, \cdot)\) n/a 21600 144
8046.2.bh \(\chi_{8046}(7, \cdot)\) n/a 97200 216
8046.2.bi \(\chi_{8046}(11, \cdot)\) n/a 194400 432

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

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_1(8046))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_1(8046)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_1(18))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(27))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(54))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(149))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(298))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(447))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(894))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(1341))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(2682))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(4023))\)\(^{\oplus 2}\)