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Properties

Label 2001.1
Level 2001
Weight 1
Dimension 84
Nonzero newspaces 2
Newform subspaces 8
Sturm bound 295680
Trace bound 1

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Defining parameters

Level: \( N \) = \( 2001 = 3 \cdot 23 \cdot 29 \)
Weight: \( k \) = \( 1 \)
Nonzero newspaces: \( 2 \)
Newform subspaces: \( 8 \)
Sturm bound: \(295680\)
Trace bound: \(1\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{1}(\Gamma_1(2001))\).

Total New Old
Modular forms 2634 1220 1414
Cusp forms 170 84 86
Eisenstein series 2464 1136 1328

The following table gives the dimensions of subspaces with specified projective image type.

\(D_n\) \(A_4\) \(S_4\) \(A_5\)
Dimension 84 0 0 0

Trace form

\( 84 q + O(q^{10}) \) \( 84 q - 84 q^{64} + 42 q^{72} - 42 q^{96} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{1}^{\mathrm{new}}(\Gamma_1(2001))\)

We only show spaces with odd 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
2001.1.b \(\chi_{2001}(1333, \cdot)\) None 0 1
2001.1.c \(\chi_{2001}(668, \cdot)\) None 0 1
2001.1.f \(\chi_{2001}(436, \cdot)\) None 0 1
2001.1.g \(\chi_{2001}(1565, \cdot)\) None 0 1
2001.1.i \(\chi_{2001}(1172, \cdot)\) 2001.1.i.a 2 2
2001.1.i.b 2
2001.1.i.c 4
2001.1.i.d 4
2001.1.j \(\chi_{2001}(70, \cdot)\) None 0 2
2001.1.p \(\chi_{2001}(254, \cdot)\) None 0 6
2001.1.q \(\chi_{2001}(574, \cdot)\) None 0 6
2001.1.t \(\chi_{2001}(806, \cdot)\) None 0 6
2001.1.u \(\chi_{2001}(22, \cdot)\) None 0 6
2001.1.w \(\chi_{2001}(173, \cdot)\) None 0 10
2001.1.x \(\chi_{2001}(88, \cdot)\) None 0 10
2001.1.ba \(\chi_{2001}(59, \cdot)\) None 0 10
2001.1.bb \(\chi_{2001}(28, \cdot)\) None 0 10
2001.1.be \(\chi_{2001}(346, \cdot)\) None 0 12
2001.1.bf \(\chi_{2001}(68, \cdot)\) 2001.1.bf.a 12 12
2001.1.bf.b 12
2001.1.bf.c 24
2001.1.bf.d 24
2001.1.bi \(\chi_{2001}(133, \cdot)\) None 0 20
2001.1.bj \(\chi_{2001}(17, \cdot)\) None 0 20
2001.1.bl \(\chi_{2001}(34, \cdot)\) None 0 60
2001.1.bm \(\chi_{2001}(110, \cdot)\) None 0 60
2001.1.bp \(\chi_{2001}(7, \cdot)\) None 0 60
2001.1.bq \(\chi_{2001}(35, \cdot)\) None 0 60
2001.1.bs \(\chi_{2001}(11, \cdot)\) None 0 120
2001.1.bt \(\chi_{2001}(31, \cdot)\) None 0 120

Decomposition of \(S_{1}^{\mathrm{old}}(\Gamma_1(2001))\) into lower level spaces

\( S_{1}^{\mathrm{old}}(\Gamma_1(2001)) \cong \) \(S_{1}^{\mathrm{new}}(\Gamma_1(23))\)\(^{\oplus 4}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(87))\)\(^{\oplus 2}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(667))\)\(^{\oplus 2}\)