Properties

Label 8048.2
Level 8048
Weight 2
Dimension 1136273
Nonzero newspaces 8
Sturm bound 8096256

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Defining parameters

Level: \( N \) = \( 8048 = 2^{4} \cdot 503 \)
Weight: \( k \) = \( 2 \)
Nonzero newspaces: \( 8 \)
Sturm bound: \(8096256\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_1(8048))\).

Total New Old
Modular forms 2031092 1140781 890311
Cusp forms 2017037 1136273 880764
Eisenstein series 14055 4508 9547

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_1(8048))\)

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 the newforms together with their dimension.

Label \(\chi\) Newforms Dimension \(\chi\) degree
8048.2.a \(\chi_{8048}(1, \cdot)\) 8048.2.a.a 1 1
8048.2.a.b 1
8048.2.a.c 1
8048.2.a.d 1
8048.2.a.e 1
8048.2.a.f 1
8048.2.a.g 1
8048.2.a.h 1
8048.2.a.i 1
8048.2.a.j 1
8048.2.a.k 1
8048.2.a.l 2
8048.2.a.m 3
8048.2.a.n 5
8048.2.a.o 5
8048.2.a.p 10
8048.2.a.q 12
8048.2.a.r 12
8048.2.a.s 21
8048.2.a.t 21
8048.2.a.u 26
8048.2.a.v 28
8048.2.a.w 29
8048.2.a.x 33
8048.2.a.y 33
8048.2.b \(\chi_{8048}(8047, \cdot)\) n/a 252 1
8048.2.c \(\chi_{8048}(4025, \cdot)\) None 0 1
8048.2.h \(\chi_{8048}(4023, \cdot)\) None 0 1
8048.2.j \(\chi_{8048}(2013, \cdot)\) n/a 2008 2
8048.2.l \(\chi_{8048}(2011, \cdot)\) n/a 2012 2
8048.2.m \(\chi_{8048}(33, \cdot)\) n/a 62750 250
8048.2.n \(\chi_{8048}(55, \cdot)\) None 0 250
8048.2.s \(\chi_{8048}(9, \cdot)\) None 0 250
8048.2.t \(\chi_{8048}(15, \cdot)\) n/a 63000 250
8048.2.u \(\chi_{8048}(19, \cdot)\) n/a 503000 500
8048.2.w \(\chi_{8048}(13, \cdot)\) n/a 503000 500

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

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_1(8048))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_1(8048)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_1(16))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(503))\)\(^{\oplus 5}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(1006))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(2012))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(4024))\)\(^{\oplus 2}\)