Properties

Label 144.14
Level 144
Weight 14
Dimension 3314
Nonzero newspaces 8
Sturm bound 16128
Trace bound 2

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Defining parameters

Level: \( N \) = \( 144 = 2^{4} \cdot 3^{2} \)
Weight: \( k \) = \( 14 \)
Nonzero newspaces: \( 8 \)
Sturm bound: \(16128\)
Trace bound: \(2\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{14}(\Gamma_1(144))\).

Total New Old
Modular forms 7600 3355 4245
Cusp forms 7376 3314 4062
Eisenstein series 224 41 183

Trace form

\( 3314 q - 6 q^{2} - 6 q^{3} + 356 q^{4} + 16895 q^{5} - 8 q^{6} + 170065 q^{7} - 1076880 q^{8} - 654478 q^{9} + 1809788 q^{10} + 8858049 q^{11} - 8 q^{12} - 26529515 q^{13} - 32258280 q^{14} + 55638477 q^{15}+ \cdots - 48339313529751 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Decomposition of \(S_{14}^{\mathrm{new}}(\Gamma_1(144))\)

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
144.14.a \(\chi_{144}(1, \cdot)\) 144.14.a.a 1 1
144.14.a.b 1
144.14.a.c 1
144.14.a.d 1
144.14.a.e 1
144.14.a.f 1
144.14.a.g 1
144.14.a.h 1
144.14.a.i 1
144.14.a.j 1
144.14.a.k 1
144.14.a.l 1
144.14.a.m 2
144.14.a.n 2
144.14.a.o 2
144.14.a.p 2
144.14.a.q 2
144.14.a.r 2
144.14.a.s 2
144.14.a.t 3
144.14.a.u 3
144.14.c \(\chi_{144}(143, \cdot)\) 144.14.c.a 2 1
144.14.c.b 8
144.14.c.c 16
144.14.d \(\chi_{144}(73, \cdot)\) None 0 1
144.14.f \(\chi_{144}(71, \cdot)\) None 0 1
144.14.i \(\chi_{144}(49, \cdot)\) n/a 154 2
144.14.k \(\chi_{144}(37, \cdot)\) n/a 258 2
144.14.l \(\chi_{144}(35, \cdot)\) n/a 208 2
144.14.p \(\chi_{144}(23, \cdot)\) None 0 2
144.14.r \(\chi_{144}(25, \cdot)\) None 0 2
144.14.s \(\chi_{144}(47, \cdot)\) n/a 156 2
144.14.u \(\chi_{144}(11, \cdot)\) n/a 1240 4
144.14.x \(\chi_{144}(13, \cdot)\) n/a 1240 4

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

Decomposition of \(S_{14}^{\mathrm{old}}(\Gamma_1(144))\) into lower level spaces

\( S_{14}^{\mathrm{old}}(\Gamma_1(144)) \cong \) \(S_{14}^{\mathrm{new}}(\Gamma_1(1))\)\(^{\oplus 15}\)\(\oplus\)\(S_{14}^{\mathrm{new}}(\Gamma_1(2))\)\(^{\oplus 12}\)\(\oplus\)\(S_{14}^{\mathrm{new}}(\Gamma_1(3))\)\(^{\oplus 10}\)\(\oplus\)\(S_{14}^{\mathrm{new}}(\Gamma_1(4))\)\(^{\oplus 9}\)\(\oplus\)\(S_{14}^{\mathrm{new}}(\Gamma_1(6))\)\(^{\oplus 8}\)\(\oplus\)\(S_{14}^{\mathrm{new}}(\Gamma_1(8))\)\(^{\oplus 6}\)\(\oplus\)\(S_{14}^{\mathrm{new}}(\Gamma_1(9))\)\(^{\oplus 5}\)\(\oplus\)\(S_{14}^{\mathrm{new}}(\Gamma_1(12))\)\(^{\oplus 6}\)\(\oplus\)\(S_{14}^{\mathrm{new}}(\Gamma_1(16))\)\(^{\oplus 3}\)\(\oplus\)\(S_{14}^{\mathrm{new}}(\Gamma_1(18))\)\(^{\oplus 4}\)\(\oplus\)\(S_{14}^{\mathrm{new}}(\Gamma_1(24))\)\(^{\oplus 4}\)\(\oplus\)\(S_{14}^{\mathrm{new}}(\Gamma_1(36))\)\(^{\oplus 3}\)\(\oplus\)\(S_{14}^{\mathrm{new}}(\Gamma_1(48))\)\(^{\oplus 2}\)\(\oplus\)\(S_{14}^{\mathrm{new}}(\Gamma_1(72))\)\(^{\oplus 2}\)