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Properties

Label 4048.2
Level 4048
Weight 2
Dimension 277604
Nonzero newspaces 32
Sturm bound 2027520

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Defining parameters

Level: \( N \) = \( 4048 = 2^{4} \cdot 11 \cdot 23 \)
Weight: \( k \) = \( 2 \)
Nonzero newspaces: \( 32 \)
Sturm bound: \(2027520\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_1(4048))\).

Total New Old
Modular forms 513040 281008 232032
Cusp forms 500721 277604 223117
Eisenstein series 12319 3404 8915

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_1(4048))\)

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
4048.2.a \(\chi_{4048}(1, \cdot)\) 4048.2.a.a 1 1
4048.2.a.b 1
4048.2.a.c 1
4048.2.a.d 1
4048.2.a.e 1
4048.2.a.f 1
4048.2.a.g 1
4048.2.a.h 1
4048.2.a.i 1
4048.2.a.j 1
4048.2.a.k 1
4048.2.a.l 1
4048.2.a.m 2
4048.2.a.n 3
4048.2.a.o 3
4048.2.a.p 3
4048.2.a.q 3
4048.2.a.r 3
4048.2.a.s 3
4048.2.a.t 3
4048.2.a.u 3
4048.2.a.v 4
4048.2.a.w 4
4048.2.a.x 4
4048.2.a.y 5
4048.2.a.z 5
4048.2.a.ba 5
4048.2.a.bb 5
4048.2.a.bc 6
4048.2.a.bd 8
4048.2.a.be 8
4048.2.a.bf 9
4048.2.a.bg 9
4048.2.d \(\chi_{4048}(2025, \cdot)\) None 0 1
4048.2.e \(\chi_{4048}(2575, \cdot)\) n/a 120 1
4048.2.h \(\chi_{4048}(2991, \cdot)\) n/a 132 1
4048.2.i \(\chi_{4048}(505, \cdot)\) None 0 1
4048.2.l \(\chi_{4048}(2529, \cdot)\) n/a 142 1
4048.2.m \(\chi_{4048}(967, \cdot)\) None 0 1
4048.2.p \(\chi_{4048}(551, \cdot)\) None 0 1
4048.2.q \(\chi_{4048}(1979, \cdot)\) n/a 1056 2
4048.2.r \(\chi_{4048}(1517, \cdot)\) n/a 1144 2
4048.2.s \(\chi_{4048}(1563, \cdot)\) n/a 960 2
4048.2.t \(\chi_{4048}(1013, \cdot)\) n/a 880 2
4048.2.y \(\chi_{4048}(1105, \cdot)\) n/a 528 4
4048.2.z \(\chi_{4048}(1655, \cdot)\) None 0 4
4048.2.bc \(\chi_{4048}(2439, \cdot)\) None 0 4
4048.2.bd \(\chi_{4048}(321, \cdot)\) n/a 568 4
4048.2.bg \(\chi_{4048}(1977, \cdot)\) None 0 4
4048.2.bh \(\chi_{4048}(415, \cdot)\) n/a 528 4
4048.2.bk \(\chi_{4048}(367, \cdot)\) n/a 576 4
4048.2.bl \(\chi_{4048}(185, \cdot)\) None 0 4
4048.2.bo \(\chi_{4048}(177, \cdot)\) n/a 1200 10
4048.2.bt \(\chi_{4048}(93, \cdot)\) n/a 4224 8
4048.2.bu \(\chi_{4048}(91, \cdot)\) n/a 4576 8
4048.2.bv \(\chi_{4048}(413, \cdot)\) n/a 4576 8
4048.2.bw \(\chi_{4048}(139, \cdot)\) n/a 4224 8
4048.2.bx \(\chi_{4048}(199, \cdot)\) None 0 10
4048.2.ca \(\chi_{4048}(87, \cdot)\) None 0 10
4048.2.cb \(\chi_{4048}(65, \cdot)\) n/a 1420 10
4048.2.ce \(\chi_{4048}(153, \cdot)\) None 0 10
4048.2.cf \(\chi_{4048}(351, \cdot)\) n/a 1440 10
4048.2.ci \(\chi_{4048}(111, \cdot)\) n/a 1200 10
4048.2.cj \(\chi_{4048}(265, \cdot)\) None 0 10
4048.2.cq \(\chi_{4048}(133, \cdot)\) n/a 9600 20
4048.2.cr \(\chi_{4048}(67, \cdot)\) n/a 9600 20
4048.2.cs \(\chi_{4048}(21, \cdot)\) n/a 11440 20
4048.2.ct \(\chi_{4048}(131, \cdot)\) n/a 11440 20
4048.2.cu \(\chi_{4048}(49, \cdot)\) n/a 5680 40
4048.2.cx \(\chi_{4048}(9, \cdot)\) None 0 40
4048.2.cy \(\chi_{4048}(15, \cdot)\) n/a 5760 40
4048.2.db \(\chi_{4048}(95, \cdot)\) n/a 5760 40
4048.2.dc \(\chi_{4048}(57, \cdot)\) None 0 40
4048.2.df \(\chi_{4048}(17, \cdot)\) n/a 5680 40
4048.2.dg \(\chi_{4048}(39, \cdot)\) None 0 40
4048.2.dj \(\chi_{4048}(103, \cdot)\) None 0 40
4048.2.dk \(\chi_{4048}(35, \cdot)\) n/a 45760 80
4048.2.dl \(\chi_{4048}(61, \cdot)\) n/a 45760 80
4048.2.dm \(\chi_{4048}(203, \cdot)\) n/a 45760 80
4048.2.dn \(\chi_{4048}(141, \cdot)\) n/a 45760 80

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

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_1(4048))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_1(4048)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_1(1))\)\(^{\oplus 20}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(2))\)\(^{\oplus 16}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(4))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(8))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(11))\)\(^{\oplus 10}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(16))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(22))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(23))\)\(^{\oplus 10}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(44))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(46))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(88))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(92))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(176))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(184))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(253))\)\(^{\oplus 5}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(368))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(506))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(1012))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(2024))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(4048))\)\(^{\oplus 1}\)