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Properties

Label 5488.2
Level 5488
Weight 2
Dimension 495720
Nonzero newspaces 24
Sturm bound 3687936

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Defining parameters

Level: \( N \) = \( 5488 = 2^{4} \cdot 7^{3} \)
Weight: \( k \) = \( 2 \)
Nonzero newspaces: \( 24 \)
Sturm bound: \(3687936\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_1(5488))\).

Total New Old
Modular forms 929628 499608 430020
Cusp forms 914341 495720 418621
Eisenstein series 15287 3888 11399

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_1(5488))\)

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
5488.2.a \(\chi_{5488}(1, \cdot)\) 5488.2.a.a 3 1
5488.2.a.b 3
5488.2.a.c 3
5488.2.a.d 3
5488.2.a.e 3
5488.2.a.f 3
5488.2.a.g 6
5488.2.a.h 6
5488.2.a.i 6
5488.2.a.j 6
5488.2.a.k 6
5488.2.a.l 6
5488.2.a.m 6
5488.2.a.n 6
5488.2.a.o 6
5488.2.a.p 6
5488.2.a.q 6
5488.2.a.r 9
5488.2.a.s 9
5488.2.a.t 9
5488.2.a.u 9
5488.2.a.v 12
5488.2.a.w 12
5488.2.b \(\chi_{5488}(2745, \cdot)\) None 0 1
5488.2.e \(\chi_{5488}(2743, \cdot)\) None 0 1
5488.2.f \(\chi_{5488}(5487, \cdot)\) n/a 144 1
5488.2.i \(\chi_{5488}(3105, \cdot)\) n/a 288 2
5488.2.j \(\chi_{5488}(1371, \cdot)\) n/a 1152 2
5488.2.m \(\chi_{5488}(1373, \cdot)\) n/a 1152 2
5488.2.p \(\chi_{5488}(1391, \cdot)\) n/a 288 2
5488.2.q \(\chi_{5488}(4135, \cdot)\) None 0 2
5488.2.t \(\chi_{5488}(361, \cdot)\) None 0 2
5488.2.u \(\chi_{5488}(785, \cdot)\) n/a 810 6
5488.2.w \(\chi_{5488}(19, \cdot)\) n/a 2304 4
5488.2.x \(\chi_{5488}(1733, \cdot)\) n/a 2304 4
5488.2.bb \(\chi_{5488}(783, \cdot)\) n/a 840 6
5488.2.bc \(\chi_{5488}(391, \cdot)\) None 0 6
5488.2.bf \(\chi_{5488}(393, \cdot)\) None 0 6
5488.2.bg \(\chi_{5488}(177, \cdot)\) n/a 1620 12
5488.2.bh \(\chi_{5488}(197, \cdot)\) n/a 6600 12
5488.2.bk \(\chi_{5488}(195, \cdot)\) n/a 6600 12
5488.2.bl \(\chi_{5488}(569, \cdot)\) None 0 12
5488.2.bo \(\chi_{5488}(215, \cdot)\) None 0 12
5488.2.bp \(\chi_{5488}(31, \cdot)\) n/a 1680 12
5488.2.bs \(\chi_{5488}(113, \cdot)\) n/a 8190 42
5488.2.bu \(\chi_{5488}(165, \cdot)\) n/a 13200 24
5488.2.bv \(\chi_{5488}(227, \cdot)\) n/a 13200 24
5488.2.bx \(\chi_{5488}(55, \cdot)\) None 0 42
5488.2.by \(\chi_{5488}(57, \cdot)\) None 0 42
5488.2.cb \(\chi_{5488}(111, \cdot)\) n/a 8232 42
5488.2.ce \(\chi_{5488}(65, \cdot)\) n/a 16380 84
5488.2.cf \(\chi_{5488}(29, \cdot)\) n/a 65688 84
5488.2.cg \(\chi_{5488}(27, \cdot)\) n/a 65688 84
5488.2.cl \(\chi_{5488}(47, \cdot)\) n/a 16464 84
5488.2.co \(\chi_{5488}(9, \cdot)\) None 0 84
5488.2.cp \(\chi_{5488}(87, \cdot)\) None 0 84
5488.2.cs \(\chi_{5488}(3, \cdot)\) n/a 131376 168
5488.2.ct \(\chi_{5488}(37, \cdot)\) n/a 131376 168

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

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_1(5488))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_1(5488)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_1(1))\)\(^{\oplus 20}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(2))\)\(^{\oplus 16}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(4))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(7))\)\(^{\oplus 15}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(8))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(14))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(16))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(28))\)\(^{\oplus 9}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(49))\)\(^{\oplus 10}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(56))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(98))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(112))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(196))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(343))\)\(^{\oplus 5}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(392))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(686))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(784))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(1372))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(2744))\)\(^{\oplus 2}\)