Defining parameters

Level: \( N \) = \( 7406 = 2 \cdot 7 \cdot 23^{2} \)
Weight: \( k \) = \( 2 \)
Nonzero newspaces: \( 16 \)
Sturm bound: \(6703488\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_1(7406))\).

Total New Old
Modular forms 1684848 533324 1151524
Cusp forms 1666897 533324 1133573
Eisenstein series 17951 0 17951

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_1(7406))\)

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
7406.2.a \(\chi_{7406}(1, \cdot)\) 7406.2.a.a 1 1
7406.2.a.b 1
7406.2.a.c 1
7406.2.a.d 1
7406.2.a.e 1
7406.2.a.f 1
7406.2.a.g 1
7406.2.a.h 1
7406.2.a.i 1
7406.2.a.j 2
7406.2.a.k 2
7406.2.a.l 2
7406.2.a.m 2
7406.2.a.n 2
7406.2.a.o 2
7406.2.a.p 2
7406.2.a.q 2
7406.2.a.r 2
7406.2.a.s 2
7406.2.a.t 3
7406.2.a.u 3
7406.2.a.v 3
7406.2.a.w 3
7406.2.a.x 3
7406.2.a.y 4
7406.2.a.z 4
7406.2.a.ba 4
7406.2.a.bb 4
7406.2.a.bc 4
7406.2.a.bd 4
7406.2.a.be 5
7406.2.a.bf 5
7406.2.a.bg 5
7406.2.a.bh 5
7406.2.a.bi 6
7406.2.a.bj 6
7406.2.a.bk 6
7406.2.a.bl 6
7406.2.a.bm 8
7406.2.a.bn 8
7406.2.a.bo 10
7406.2.a.bp 10
7406.2.a.bq 12
7406.2.a.br 12
7406.2.a.bs 20
7406.2.a.bt 20
7406.2.a.bu 20
7406.2.a.bv 20
7406.2.c \(\chi_{7406}(7405, \cdot)\) n/a 336 1
7406.2.e \(\chi_{7406}(1059, \cdot)\) n/a 672 2
7406.2.g \(\chi_{7406}(4231, \cdot)\) n/a 672 2
7406.2.i \(\chi_{7406}(995, \cdot)\) n/a 2520 10
7406.2.k \(\chi_{7406}(195, \cdot)\) n/a 3360 10
7406.2.m \(\chi_{7406}(323, \cdot)\) n/a 6072 22
7406.2.n \(\chi_{7406}(177, \cdot)\) n/a 6720 20
7406.2.p \(\chi_{7406}(321, \cdot)\) n/a 8096 22
7406.2.s \(\chi_{7406}(411, \cdot)\) n/a 6720 20
7406.2.u \(\chi_{7406}(93, \cdot)\) n/a 16192 44
7406.2.w \(\chi_{7406}(45, \cdot)\) n/a 16192 44
7406.2.y \(\chi_{7406}(29, \cdot)\) n/a 60720 220
7406.2.ba \(\chi_{7406}(83, \cdot)\) n/a 80960 220
7406.2.bc \(\chi_{7406}(9, \cdot)\) n/a 161920 440
7406.2.be \(\chi_{7406}(5, \cdot)\) n/a 161920 440

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

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_1(7406))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_1(7406)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_1(1))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(2))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(7))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(14))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(23))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(46))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(161))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(322))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(529))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(1058))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(3703))\)\(^{\oplus 2}\)