Properties

Label 4011.2
Level 4011
Weight 2
Dimension 417611
Nonzero newspaces 32
Sturm bound 2334720

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Defining parameters

Level: \( N \) = \( 4011 = 3 \cdot 7 \cdot 191 \)
Weight: \( k \) = \( 2 \)
Nonzero newspaces: \( 32 \)
Sturm bound: \(2334720\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_1(4011))\).

Total New Old
Modular forms 588240 421387 166853
Cusp forms 579121 417611 161510
Eisenstein series 9119 3776 5343

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_1(4011))\)

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
4011.2.a \(\chi_{4011}(1, \cdot)\) 4011.2.a.a 1 1
4011.2.a.b 1
4011.2.a.c 1
4011.2.a.d 1
4011.2.a.e 3
4011.2.a.f 18
4011.2.a.g 18
4011.2.a.h 19
4011.2.a.i 19
4011.2.a.j 26
4011.2.a.k 27
4011.2.a.l 28
4011.2.a.m 29
4011.2.c \(\chi_{4011}(2864, \cdot)\) n/a 384 1
4011.2.d \(\chi_{4011}(3821, \cdot)\) n/a 508 1
4011.2.f \(\chi_{4011}(1336, \cdot)\) n/a 256 1
4011.2.i \(\chi_{4011}(2293, \cdot)\) n/a 508 2
4011.2.j \(\chi_{4011}(421, \cdot)\) n/a 768 4
4011.2.m \(\chi_{4011}(1909, \cdot)\) n/a 512 2
4011.2.o \(\chi_{4011}(383, \cdot)\) n/a 1012 2
4011.2.p \(\chi_{4011}(1145, \cdot)\) n/a 1016 2
4011.2.r \(\chi_{4011}(580, \cdot)\) n/a 1024 4
4011.2.v \(\chi_{4011}(1037, \cdot)\) n/a 1536 4
4011.2.w \(\chi_{4011}(230, \cdot)\) n/a 2032 4
4011.2.y \(\chi_{4011}(109, \cdot)\) n/a 2048 8
4011.2.z \(\chi_{4011}(316, \cdot)\) n/a 3456 18
4011.2.bb \(\chi_{4011}(803, \cdot)\) n/a 4064 8
4011.2.bc \(\chi_{4011}(389, \cdot)\) n/a 4064 8
4011.2.bg \(\chi_{4011}(82, \cdot)\) n/a 2048 8
4011.2.bj \(\chi_{4011}(55, \cdot)\) n/a 4608 18
4011.2.bl \(\chi_{4011}(125, \cdot)\) n/a 9144 18
4011.2.bm \(\chi_{4011}(155, \cdot)\) n/a 6912 18
4011.2.bo \(\chi_{4011}(25, \cdot)\) n/a 9216 36
4011.2.bp \(\chi_{4011}(43, \cdot)\) n/a 13824 72
4011.2.br \(\chi_{4011}(11, \cdot)\) n/a 18288 36
4011.2.bs \(\chi_{4011}(5, \cdot)\) n/a 18288 36
4011.2.bu \(\chi_{4011}(31, \cdot)\) n/a 9216 36
4011.2.by \(\chi_{4011}(20, \cdot)\) n/a 36576 72
4011.2.bz \(\chi_{4011}(29, \cdot)\) n/a 27648 72
4011.2.cd \(\chi_{4011}(76, \cdot)\) n/a 18432 72
4011.2.ce \(\chi_{4011}(4, \cdot)\) n/a 36864 144
4011.2.cf \(\chi_{4011}(19, \cdot)\) n/a 36864 144
4011.2.cj \(\chi_{4011}(44, \cdot)\) n/a 73152 144
4011.2.ck \(\chi_{4011}(17, \cdot)\) n/a 73152 144

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

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_1(4011))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_1(4011)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_1(21))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(191))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(573))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(1337))\)\(^{\oplus 2}\)