Properties

Label 7569.2
Level 7569
Weight 2
Dimension 1668639
Nonzero newspaces 24
Sturm bound 8477280

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Defining parameters

Level: \( N \) = \( 7569 = 3^{2} \cdot 29^{2} \)
Weight: \( k \) = \( 2 \)
Nonzero newspaces: \( 24 \)
Sturm bound: \(8477280\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_1(7569))\).

Total New Old
Modular forms 2128952 1678976 449976
Cusp forms 2109689 1668639 441050
Eisenstein series 19263 10337 8926

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_1(7569))\)

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
7569.2.a \(\chi_{7569}(1, \cdot)\) 7569.2.a.a 1 1
7569.2.a.b 1
7569.2.a.c 2
7569.2.a.d 2
7569.2.a.e 2
7569.2.a.f 2
7569.2.a.g 2
7569.2.a.h 2
7569.2.a.i 2
7569.2.a.j 2
7569.2.a.k 2
7569.2.a.l 2
7569.2.a.m 2
7569.2.a.n 2
7569.2.a.o 2
7569.2.a.p 3
7569.2.a.q 3
7569.2.a.r 3
7569.2.a.s 3
7569.2.a.t 3
7569.2.a.u 4
7569.2.a.v 4
7569.2.a.w 4
7569.2.a.x 4
7569.2.a.y 6
7569.2.a.z 6
7569.2.a.ba 6
7569.2.a.bb 6
7569.2.a.bc 6
7569.2.a.bd 8
7569.2.a.be 8
7569.2.a.bf 8
7569.2.a.bg 8
7569.2.a.bh 8
7569.2.a.bi 8
7569.2.a.bj 9
7569.2.a.bk 9
7569.2.a.bl 9
7569.2.a.bm 9
7569.2.a.bn 12
7569.2.a.bo 12
7569.2.a.bp 12
7569.2.a.bq 12
7569.2.a.br 12
7569.2.a.bs 12
7569.2.a.bt 12
7569.2.a.bu 16
7569.2.a.bv 16
7569.2.a.bw 36
7569.2.c \(\chi_{7569}(4204, \cdot)\) n/a 324 1
7569.2.e \(\chi_{7569}(2524, \cdot)\) n/a 1568 2
7569.2.g \(\chi_{7569}(800, \cdot)\) n/a 540 2
7569.2.i \(\chi_{7569}(1681, \cdot)\) n/a 1568 2
7569.2.k \(\chi_{7569}(190, \cdot)\) n/a 1950 6
7569.2.l \(\chi_{7569}(41, \cdot)\) n/a 3136 4
7569.2.o \(\chi_{7569}(1108, \cdot)\) n/a 1944 6
7569.2.q \(\chi_{7569}(571, \cdot)\) n/a 9408 12
7569.2.r \(\chi_{7569}(467, \cdot)\) n/a 3240 12
7569.2.t \(\chi_{7569}(262, \cdot)\) n/a 10108 28
7569.2.v \(\chi_{7569}(196, \cdot)\) n/a 9408 12
7569.2.y \(\chi_{7569}(28, \cdot)\) n/a 10136 28
7569.2.bb \(\chi_{7569}(14, \cdot)\) n/a 18816 24
7569.2.bc \(\chi_{7569}(88, \cdot)\) n/a 48608 56
7569.2.bd \(\chi_{7569}(17, \cdot)\) n/a 16240 56
7569.2.bg \(\chi_{7569}(115, \cdot)\) n/a 48608 56
7569.2.bi \(\chi_{7569}(82, \cdot)\) n/a 60648 168
7569.2.bk \(\chi_{7569}(104, \cdot)\) n/a 97216 112
7569.2.bm \(\chi_{7569}(64, \cdot)\) n/a 60816 168
7569.2.bo \(\chi_{7569}(7, \cdot)\) n/a 291648 336
7569.2.bq \(\chi_{7569}(8, \cdot)\) n/a 97440 336
7569.2.bs \(\chi_{7569}(4, \cdot)\) n/a 291648 336
7569.2.bu \(\chi_{7569}(2, \cdot)\) n/a 583296 672

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

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_1(7569))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_1(7569)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_1(1))\)\(^{\oplus 9}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(3))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(9))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(29))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(87))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(261))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(841))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(2523))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(7569))\)\(^{\oplus 1}\)