Properties

Label 4096.2
Level 4096
Weight 2
Dimension 293824
Nonzero newspaces 10
Sturm bound 2097152

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Defining parameters

Level: \( N \) = \( 4096 = 2^{12} \)
Weight: \( k \) = \( 2 \)
Nonzero newspaces: \( 10 \)
Sturm bound: \(2097152\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_1(4096))\).

Total New Old
Modular forms 528128 296000 232128
Cusp forms 520449 293824 226625
Eisenstein series 7679 2176 5503

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_1(4096))\)

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
4096.2.a \(\chi_{4096}(1, \cdot)\) 4096.2.a.a 4 1
4096.2.a.b 4
4096.2.a.c 4
4096.2.a.d 4
4096.2.a.e 4
4096.2.a.f 4
4096.2.a.g 4
4096.2.a.h 4
4096.2.a.i 8
4096.2.a.j 8
4096.2.a.k 8
4096.2.a.l 8
4096.2.a.m 8
4096.2.a.n 8
4096.2.a.o 8
4096.2.a.p 8
4096.2.a.q 8
4096.2.a.r 8
4096.2.a.s 8
4096.2.b \(\chi_{4096}(2049, \cdot)\) n/a 120 1
4096.2.e \(\chi_{4096}(1025, \cdot)\) n/a 240 2
4096.2.g \(\chi_{4096}(513, \cdot)\) n/a 480 4
4096.2.i \(\chi_{4096}(257, \cdot)\) n/a 1024 8
4096.2.k \(\chi_{4096}(129, \cdot)\) n/a 1920 16
4096.2.m \(\chi_{4096}(65, \cdot)\) n/a 3968 32
4096.2.o \(\chi_{4096}(33, \cdot)\) n/a 8064 64
4096.2.q \(\chi_{4096}(17, \cdot)\) n/a 16256 128
4096.2.s \(\chi_{4096}(9, \cdot)\) None 0 256
4096.2.u \(\chi_{4096}(5, \cdot)\) n/a 261632 512

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

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_1(4096))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_1(4096)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_1(16))\)\(^{\oplus 9}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(32))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(64))\)\(^{\oplus 7}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(128))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(256))\)\(^{\oplus 5}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(512))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(1024))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(2048))\)\(^{\oplus 2}\)