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Properties

Label 8381.2
Level 8381
Weight 2
Dimension 2876159
Nonzero newspaces 40
Sturm bound 11652480

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Defining parameters

Level: \( N \) = \( 8381 = 17^{2} \cdot 29 \)
Weight: \( k \) = \( 2 \)
Nonzero newspaces: \( 40 \)
Sturm bound: \(11652480\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_1(8381))\).

Total New Old
Modular forms 2924320 2896057 28263
Cusp forms 2901921 2876159 25762
Eisenstein series 22399 19898 2501

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_1(8381))\)

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
8381.2.a \(\chi_{8381}(1, \cdot)\) 8381.2.a.a 1 1
8381.2.a.b 1
8381.2.a.c 1
8381.2.a.d 1
8381.2.a.e 2
8381.2.a.f 2
8381.2.a.g 4
8381.2.a.h 5
8381.2.a.i 6
8381.2.a.j 8
8381.2.a.k 10
8381.2.a.l 14
8381.2.a.m 14
8381.2.a.n 21
8381.2.a.o 21
8381.2.a.p 21
8381.2.a.q 21
8381.2.a.r 42
8381.2.a.s 42
8381.2.a.t 48
8381.2.a.u 48
8381.2.a.v 66
8381.2.a.w 66
8381.2.a.x 84
8381.2.a.y 84
8381.2.b \(\chi_{8381}(579, \cdot)\) n/a 662 1
8381.2.c \(\chi_{8381}(8380, \cdot)\) n/a 660 1
8381.2.d \(\chi_{8381}(7802, \cdot)\) n/a 630 1
8381.2.e \(\chi_{8381}(2350, \cdot)\) n/a 1260 2
8381.2.j \(\chi_{8381}(2928, \cdot)\) n/a 1320 2
8381.2.k \(\chi_{8381}(1446, \cdot)\) n/a 3978 6
8381.2.m \(\chi_{8381}(1913, \cdot)\) n/a 2648 4
8381.2.n \(\chi_{8381}(1335, \cdot)\) n/a 2520 4
8381.2.p \(\chi_{8381}(866, \cdot)\) n/a 3972 6
8381.2.q \(\chi_{8381}(1733, \cdot)\) n/a 3960 6
8381.2.r \(\chi_{8381}(2313, \cdot)\) n/a 3972 6
8381.2.t \(\chi_{8381}(1380, \cdot)\) n/a 5288 8
8381.2.u \(\chi_{8381}(75, \cdot)\) n/a 5288 8
8381.2.w \(\chi_{8381}(494, \cdot)\) n/a 11424 16
8381.2.x \(\chi_{8381}(38, \cdot)\) n/a 7920 12
8381.2.bc \(\chi_{8381}(616, \cdot)\) n/a 7944 12
8381.2.bd \(\chi_{8381}(407, \cdot)\) n/a 11424 16
8381.2.be \(\chi_{8381}(492, \cdot)\) n/a 12224 16
8381.2.bf \(\chi_{8381}(86, \cdot)\) n/a 12224 16
8381.2.bh \(\chi_{8381}(110, \cdot)\) n/a 15840 24
8381.2.bi \(\chi_{8381}(179, \cdot)\) n/a 15888 24
8381.2.bk \(\chi_{8381}(115, \cdot)\) n/a 24448 32
8381.2.bp \(\chi_{8381}(30, \cdot)\) n/a 22848 32
8381.2.br \(\chi_{8381}(40, \cdot)\) n/a 31728 48
8381.2.bs \(\chi_{8381}(224, \cdot)\) n/a 31728 48
8381.2.bu \(\chi_{8381}(52, \cdot)\) n/a 73152 96
8381.2.bw \(\chi_{8381}(59, \cdot)\) n/a 45696 64
8381.2.bx \(\chi_{8381}(144, \cdot)\) n/a 48768 64
8381.2.bz \(\chi_{8381}(35, \cdot)\) n/a 73344 96
8381.2.ca \(\chi_{8381}(33, \cdot)\) n/a 73344 96
8381.2.cb \(\chi_{8381}(16, \cdot)\) n/a 73152 96
8381.2.cd \(\chi_{8381}(12, \cdot)\) n/a 97664 128
8381.2.ce \(\chi_{8381}(41, \cdot)\) n/a 97664 128
8381.2.cg \(\chi_{8381}(81, \cdot)\) n/a 146304 192
8381.2.cl \(\chi_{8381}(4, \cdot)\) n/a 146688 192
8381.2.cn \(\chi_{8381}(9, \cdot)\) n/a 292608 384
8381.2.co \(\chi_{8381}(25, \cdot)\) n/a 293376 384
8381.2.cr \(\chi_{8381}(3, \cdot)\) n/a 585984 768
8381.2.cs \(\chi_{8381}(11, \cdot)\) n/a 585984 768

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

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_1(8381))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_1(8381)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_1(17))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(29))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(289))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(493))\)\(^{\oplus 2}\)