Defining parameters
Level: | \( N \) | = | \( 450 = 2 \cdot 3^{2} \cdot 5^{2} \) |
Weight: | \( k \) | = | \( 3 \) |
Nonzero newspaces: | \( 12 \) | ||
Sturm bound: | \(32400\) | ||
Trace bound: | \(4\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{3}(\Gamma_1(450))\).
Total | New | Old | |
---|---|---|---|
Modular forms | 11248 | 2628 | 8620 |
Cusp forms | 10352 | 2628 | 7724 |
Eisenstein series | 896 | 0 | 896 |
Trace form
Decomposition of \(S_{3}^{\mathrm{new}}(\Gamma_1(450))\)
We only show spaces with odd 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 |
---|---|---|---|---|
450.3.b | \(\chi_{450}(449, \cdot)\) | 450.3.b.a | 4 | 1 |
450.3.b.b | 4 | |||
450.3.b.c | 4 | |||
450.3.d | \(\chi_{450}(251, \cdot)\) | 450.3.d.a | 2 | 1 |
450.3.d.b | 2 | |||
450.3.d.c | 2 | |||
450.3.d.d | 2 | |||
450.3.d.e | 2 | |||
450.3.d.f | 2 | |||
450.3.d.g | 2 | |||
450.3.g | \(\chi_{450}(307, \cdot)\) | 450.3.g.a | 2 | 2 |
450.3.g.b | 2 | |||
450.3.g.c | 2 | |||
450.3.g.d | 2 | |||
450.3.g.e | 2 | |||
450.3.g.f | 4 | |||
450.3.g.g | 4 | |||
450.3.g.h | 4 | |||
450.3.g.i | 4 | |||
450.3.g.j | 4 | |||
450.3.i | \(\chi_{450}(101, \cdot)\) | 450.3.i.a | 4 | 2 |
450.3.i.b | 4 | |||
450.3.i.c | 4 | |||
450.3.i.d | 16 | |||
450.3.i.e | 16 | |||
450.3.i.f | 16 | |||
450.3.i.g | 16 | |||
450.3.k | \(\chi_{450}(149, \cdot)\) | 450.3.k.a | 8 | 2 |
450.3.k.b | 32 | |||
450.3.k.c | 32 | |||
450.3.m | \(\chi_{450}(89, \cdot)\) | 450.3.m.a | 80 | 4 |
450.3.n | \(\chi_{450}(71, \cdot)\) | 450.3.n.a | 32 | 4 |
450.3.n.b | 48 | |||
450.3.o | \(\chi_{450}(7, \cdot)\) | n/a | 144 | 4 |
450.3.r | \(\chi_{450}(37, \cdot)\) | n/a | 200 | 8 |
450.3.t | \(\chi_{450}(11, \cdot)\) | n/a | 480 | 8 |
450.3.u | \(\chi_{450}(29, \cdot)\) | n/a | 480 | 8 |
450.3.x | \(\chi_{450}(13, \cdot)\) | n/a | 960 | 16 |
"n/a" means that newforms for that character have not been added to the database yet
Decomposition of \(S_{3}^{\mathrm{old}}(\Gamma_1(450))\) into lower level spaces
\( S_{3}^{\mathrm{old}}(\Gamma_1(450)) \cong \) \(S_{3}^{\mathrm{new}}(\Gamma_1(9))\)\(^{\oplus 6}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(\Gamma_1(10))\)\(^{\oplus 6}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(\Gamma_1(15))\)\(^{\oplus 8}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(\Gamma_1(18))\)\(^{\oplus 3}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(\Gamma_1(25))\)\(^{\oplus 6}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(\Gamma_1(30))\)\(^{\oplus 4}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(\Gamma_1(45))\)\(^{\oplus 4}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(\Gamma_1(50))\)\(^{\oplus 3}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(\Gamma_1(75))\)\(^{\oplus 4}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(\Gamma_1(90))\)\(^{\oplus 2}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(\Gamma_1(150))\)\(^{\oplus 2}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(\Gamma_1(225))\)\(^{\oplus 2}\)