Properties

Label 4012.2
Level 4012
Weight 2
Dimension 288414
Nonzero newspaces 20
Sturm bound 2004480

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Defining parameters

Level: \( N \) = \( 4012 = 2^{2} \cdot 17 \cdot 59 \)
Weight: \( k \) = \( 2 \)
Nonzero newspaces: \( 20 \)
Sturm bound: \(2004480\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_1(4012))\).

Total New Old
Modular forms 505760 291830 213930
Cusp forms 496481 288414 208067
Eisenstein series 9279 3416 5863

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_1(4012))\)

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
4012.2.a \(\chi_{4012}(1, \cdot)\) 4012.2.a.a 1 1
4012.2.a.b 1
4012.2.a.c 1
4012.2.a.d 2
4012.2.a.e 2
4012.2.a.f 3
4012.2.a.g 12
4012.2.a.h 15
4012.2.a.i 18
4012.2.a.j 21
4012.2.b \(\chi_{4012}(237, \cdot)\) 4012.2.b.a 40 1
4012.2.b.b 46
4012.2.e \(\chi_{4012}(3775, \cdot)\) n/a 480 1
4012.2.f \(\chi_{4012}(4011, \cdot)\) n/a 536 1
4012.2.j \(\chi_{4012}(1415, \cdot)\) n/a 1072 2
4012.2.k \(\chi_{4012}(1653, \cdot)\) n/a 172 2
4012.2.n \(\chi_{4012}(1181, \cdot)\) n/a 352 4
4012.2.o \(\chi_{4012}(943, \cdot)\) n/a 2144 4
4012.2.q \(\chi_{4012}(827, \cdot)\) n/a 4176 8
4012.2.t \(\chi_{4012}(589, \cdot)\) n/a 720 8
4012.2.u \(\chi_{4012}(137, \cdot)\) n/a 2240 28
4012.2.x \(\chi_{4012}(67, \cdot)\) n/a 15008 28
4012.2.y \(\chi_{4012}(103, \cdot)\) n/a 13440 28
4012.2.bb \(\chi_{4012}(169, \cdot)\) n/a 2520 28
4012.2.bd \(\chi_{4012}(21, \cdot)\) n/a 5040 56
4012.2.be \(\chi_{4012}(47, \cdot)\) n/a 30016 56
4012.2.bh \(\chi_{4012}(43, \cdot)\) n/a 60032 112
4012.2.bi \(\chi_{4012}(9, \cdot)\) n/a 10080 112
4012.2.bk \(\chi_{4012}(37, \cdot)\) n/a 20160 224
4012.2.bn \(\chi_{4012}(3, \cdot)\) n/a 120064 224

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

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_1(4012))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_1(4012)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_1(17))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(34))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(59))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(68))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(118))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(236))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(1003))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(2006))\)\(^{\oplus 2}\)