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

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

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 the 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

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

Hecke Characteristic Polynomials

$p$ $F_p(T)$
$2$ (\( ( 1 + T )^{2}( 1 + T^{2} ) \))(\( ( 1 - T )^{2}( 1 + T^{2} ) \))(\( ( 1 + T + T^{2} )^{2}( 1 - T^{2} + T^{4} ) \))(\( ( 1 - T + T^{2} )^{2}( 1 - T^{2} + T^{4} ) \))(\( ( 1 + T^{2} )^{6}( 1 + T + T^{2} + T^{3} + T^{4} + T^{5} + T^{6} )^{2} \))(\( ( 1 + T^{2} )^{6}( 1 - T + T^{2} - T^{3} + T^{4} - T^{5} + T^{6} )^{2} \))(\( ( 1 - T^{2} + T^{4} )^{6}( 1 + T - T^{3} - T^{4} + T^{6} - T^{8} - T^{9} + T^{11} + T^{12} )^{2} \))(\( ( 1 - T^{2} + T^{4} )^{6}( 1 - T + T^{3} - T^{4} + T^{6} - T^{8} + T^{9} - T^{11} + T^{12} )^{2} \))
$3$ (\( ( 1 - T )^{2} \))(\( 1 + T^{2} \))(\( 1 - T^{2} + T^{4} \))(\( ( 1 + T + T^{2} )^{2} \))(\( 1 - T^{2} + T^{4} - T^{6} + T^{8} - T^{10} + T^{12} \))(\( ( 1 + T + T^{2} + T^{3} + T^{4} + T^{5} + T^{6} )^{2} \))(\( ( 1 - T + T^{3} - T^{4} + T^{6} - T^{8} + T^{9} - T^{11} + T^{12} )^{2} \))(\( 1 + T^{2} - T^{6} - T^{8} + T^{12} - T^{16} - T^{18} + T^{22} + T^{24} \))
$5$ (\( ( 1 - T )^{2}( 1 + T )^{2} \))(\( ( 1 - T )^{2}( 1 + T )^{2} \))(\( ( 1 - T )^{4}( 1 + T )^{4} \))(\( ( 1 - T )^{4}( 1 + T )^{4} \))(\( ( 1 - T + T^{2} - T^{3} + T^{4} - T^{5} + T^{6} )^{2}( 1 + T + T^{2} + T^{3} + T^{4} + T^{5} + T^{6} )^{2} \))(\( ( 1 - T + T^{2} - T^{3} + T^{4} - T^{5} + T^{6} )^{2}( 1 + T + T^{2} + T^{3} + T^{4} + T^{5} + T^{6} )^{2} \))(\( ( 1 - T + T^{2} - T^{3} + T^{4} - T^{5} + T^{6} )^{4}( 1 + T + T^{2} + T^{3} + T^{4} + T^{5} + T^{6} )^{4} \))(\( ( 1 - T + T^{2} - T^{3} + T^{4} - T^{5} + T^{6} )^{4}( 1 + T + T^{2} + T^{3} + T^{4} + T^{5} + T^{6} )^{4} \))
$7$ (\( ( 1 - T )^{2}( 1 + T )^{2} \))(\( ( 1 - T )^{2}( 1 + T )^{2} \))(\( ( 1 - T )^{4}( 1 + T )^{4} \))(\( ( 1 - T )^{4}( 1 + T )^{4} \))(\( ( 1 - T + T^{2} - T^{3} + T^{4} - T^{5} + T^{6} )^{2}( 1 + T + T^{2} + T^{3} + T^{4} + T^{5} + T^{6} )^{2} \))(\( ( 1 - T + T^{2} - T^{3} + T^{4} - T^{5} + T^{6} )^{2}( 1 + T + T^{2} + T^{3} + T^{4} + T^{5} + T^{6} )^{2} \))(\( ( 1 - T + T^{2} - T^{3} + T^{4} - T^{5} + T^{6} )^{4}( 1 + T + T^{2} + T^{3} + T^{4} + T^{5} + T^{6} )^{4} \))(\( ( 1 - T + T^{2} - T^{3} + T^{4} - T^{5} + T^{6} )^{4}( 1 + T + T^{2} + T^{3} + T^{4} + T^{5} + T^{6} )^{4} \))
$11$ (\( 1 + T^{4} \))(\( 1 + T^{4} \))(\( ( 1 + T^{4} )^{2} \))(\( ( 1 + T^{4} )^{2} \))(\( 1 - T^{4} + T^{8} - T^{12} + T^{16} - T^{20} + T^{24} \))(\( 1 - T^{4} + T^{8} - T^{12} + T^{16} - T^{20} + T^{24} \))(\( ( 1 - T^{4} + T^{8} - T^{12} + T^{16} - T^{20} + T^{24} )^{2} \))(\( ( 1 - T^{4} + T^{8} - T^{12} + T^{16} - T^{20} + T^{24} )^{2} \))
$13$ (\( ( 1 + T^{2} )^{2} \))(\( ( 1 + T^{2} )^{2} \))(\( ( 1 - T^{2} + T^{4} )^{2} \))(\( ( 1 - T^{2} + T^{4} )^{2} \))(\( ( 1 - T^{2} + T^{4} - T^{6} + T^{8} - T^{10} + T^{12} )^{2} \))(\( ( 1 - T^{2} + T^{4} - T^{6} + T^{8} - T^{10} + T^{12} )^{2} \))(\( ( 1 + T^{2} - T^{6} - T^{8} + T^{12} - T^{16} - T^{18} + T^{22} + T^{24} )^{2} \))(\( ( 1 + T^{2} - T^{6} - T^{8} + T^{12} - T^{16} - T^{18} + T^{22} + T^{24} )^{2} \))
$17$ (\( 1 + T^{4} \))(\( 1 + T^{4} \))(\( ( 1 + T^{4} )^{2} \))(\( ( 1 + T^{4} )^{2} \))(\( ( 1 + T^{4} )^{6} \))(\( ( 1 + T^{4} )^{6} \))(\( ( 1 + T^{4} )^{12} \))(\( ( 1 + T^{4} )^{12} \))
$19$ (\( 1 + T^{4} \))(\( 1 + T^{4} \))(\( ( 1 + T^{4} )^{2} \))(\( ( 1 + T^{4} )^{2} \))(\( 1 - T^{4} + T^{8} - T^{12} + T^{16} - T^{20} + T^{24} \))(\( 1 - T^{4} + T^{8} - T^{12} + T^{16} - T^{20} + T^{24} \))(\( ( 1 - T^{4} + T^{8} - T^{12} + T^{16} - T^{20} + T^{24} )^{2} \))(\( ( 1 - T^{4} + T^{8} - T^{12} + T^{16} - T^{20} + T^{24} )^{2} \))
$23$ (\( 1 + T^{2} \))(\( 1 + T^{2} \))(\( ( 1 + T^{2} )^{2} \))(\( ( 1 + T^{2} )^{2} \))(\( 1 - T^{2} + T^{4} - T^{6} + T^{8} - T^{10} + T^{12} \))(\( 1 - T^{2} + T^{4} - T^{6} + T^{8} - T^{10} + T^{12} \))(\( ( 1 - T^{2} + T^{4} - T^{6} + T^{8} - T^{10} + T^{12} )^{2} \))(\( ( 1 - T^{2} + T^{4} - T^{6} + T^{8} - T^{10} + T^{12} )^{2} \))
$29$ (\( 1 + T^{2} \))(\( 1 + T^{2} \))(\( 1 - T^{2} + T^{4} \))(\( 1 - T^{2} + T^{4} \))(\( 1 - T^{2} + T^{4} - T^{6} + T^{8} - T^{10} + T^{12} \))(\( 1 - T^{2} + T^{4} - T^{6} + T^{8} - T^{10} + T^{12} \))(\( 1 + T^{2} - T^{6} - T^{8} + T^{12} - T^{16} - T^{18} + T^{22} + T^{24} \))(\( 1 + T^{2} - T^{6} - T^{8} + T^{12} - T^{16} - T^{18} + T^{22} + T^{24} \))
$31$ (\( ( 1 + T )^{2}( 1 + T^{2} ) \))(\( ( 1 + T )^{2}( 1 + T^{2} ) \))(\( ( 1 - T + T^{2} )^{2}( 1 - T^{2} + T^{4} ) \))(\( ( 1 - T + T^{2} )^{2}( 1 - T^{2} + T^{4} ) \))(\( ( 1 - T + T^{2} - T^{3} + T^{4} - T^{5} + T^{6} )^{2}( 1 - T^{2} + T^{4} - T^{6} + T^{8} - T^{10} + T^{12} ) \))(\( ( 1 - T + T^{2} - T^{3} + T^{4} - T^{5} + T^{6} )^{2}( 1 - T^{2} + T^{4} - T^{6} + T^{8} - T^{10} + T^{12} ) \))(\( ( 1 + T - T^{3} - T^{4} + T^{6} - T^{8} - T^{9} + T^{11} + T^{12} )^{2}( 1 + T^{2} - T^{6} - T^{8} + T^{12} - T^{16} - T^{18} + T^{22} + T^{24} ) \))(\( ( 1 + T - T^{3} - T^{4} + T^{6} - T^{8} - T^{9} + T^{11} + T^{12} )^{2}( 1 + T^{2} - T^{6} - T^{8} + T^{12} - T^{16} - T^{18} + T^{22} + T^{24} ) \))
$37$ (\( 1 + T^{4} \))(\( 1 + T^{4} \))(\( ( 1 + T^{4} )^{2} \))(\( ( 1 + T^{4} )^{2} \))(\( 1 - T^{4} + T^{8} - T^{12} + T^{16} - T^{20} + T^{24} \))(\( 1 - T^{4} + T^{8} - T^{12} + T^{16} - T^{20} + T^{24} \))(\( ( 1 - T^{4} + T^{8} - T^{12} + T^{16} - T^{20} + T^{24} )^{2} \))(\( ( 1 - T^{4} + T^{8} - T^{12} + T^{16} - T^{20} + T^{24} )^{2} \))
$41$ (\( ( 1 - T )^{2}( 1 + T^{2} ) \))(\( ( 1 + T )^{2}( 1 + T^{2} ) \))(\( ( 1 - T + T^{2} )^{2}( 1 - T^{2} + T^{4} ) \))(\( ( 1 + T + T^{2} )^{2}( 1 - T^{2} + T^{4} ) \))(\( ( 1 - T + T^{2} - T^{3} + T^{4} - T^{5} + T^{6} )^{2}( 1 - T^{2} + T^{4} - T^{6} + T^{8} - T^{10} + T^{12} ) \))(\( ( 1 + T + T^{2} + T^{3} + T^{4} + T^{5} + T^{6} )^{2}( 1 - T^{2} + T^{4} - T^{6} + T^{8} - T^{10} + T^{12} ) \))(\( ( 1 - T + T^{3} - T^{4} + T^{6} - T^{8} + T^{9} - T^{11} + T^{12} )^{2}( 1 + T^{2} - T^{6} - T^{8} + T^{12} - T^{16} - T^{18} + T^{22} + T^{24} ) \))(\( ( 1 + T - T^{3} - T^{4} + T^{6} - T^{8} - T^{9} + T^{11} + T^{12} )^{2}( 1 + T^{2} - T^{6} - T^{8} + T^{12} - T^{16} - T^{18} + T^{22} + T^{24} ) \))
$43$ (\( 1 + T^{4} \))(\( 1 + T^{4} \))(\( ( 1 + T^{4} )^{2} \))(\( ( 1 + T^{4} )^{2} \))(\( 1 - T^{4} + T^{8} - T^{12} + T^{16} - T^{20} + T^{24} \))(\( 1 - T^{4} + T^{8} - T^{12} + T^{16} - T^{20} + T^{24} \))(\( ( 1 - T^{4} + T^{8} - T^{12} + T^{16} - T^{20} + T^{24} )^{2} \))(\( ( 1 - T^{4} + T^{8} - T^{12} + T^{16} - T^{20} + T^{24} )^{2} \))
$47$ (\( ( 1 + T )^{2}( 1 + T^{2} ) \))(\( ( 1 - T )^{2}( 1 + T^{2} ) \))(\( ( 1 + T + T^{2} )^{2}( 1 - T^{2} + T^{4} ) \))(\( ( 1 - T + T^{2} )^{2}( 1 - T^{2} + T^{4} ) \))(\( ( 1 + T + T^{2} + T^{3} + T^{4} + T^{5} + T^{6} )^{2}( 1 - T^{2} + T^{4} - T^{6} + T^{8} - T^{10} + T^{12} ) \))(\( ( 1 - T + T^{2} - T^{3} + T^{4} - T^{5} + T^{6} )^{2}( 1 - T^{2} + T^{4} - T^{6} + T^{8} - T^{10} + T^{12} ) \))(\( ( 1 + T - T^{3} - T^{4} + T^{6} - T^{8} - T^{9} + T^{11} + T^{12} )^{2}( 1 + T^{2} - T^{6} - T^{8} + T^{12} - T^{16} - T^{18} + T^{22} + T^{24} ) \))(\( ( 1 - T + T^{3} - T^{4} + T^{6} - T^{8} + T^{9} - T^{11} + T^{12} )^{2}( 1 + T^{2} - T^{6} - T^{8} + T^{12} - T^{16} - T^{18} + T^{22} + T^{24} ) \))
$53$ (\( ( 1 + T^{2} )^{2} \))(\( ( 1 + T^{2} )^{2} \))(\( ( 1 + T^{2} )^{4} \))(\( ( 1 + T^{2} )^{4} \))(\( ( 1 - T^{2} + T^{4} - T^{6} + T^{8} - T^{10} + T^{12} )^{2} \))(\( ( 1 - T^{2} + T^{4} - T^{6} + T^{8} - T^{10} + T^{12} )^{2} \))(\( ( 1 - T^{2} + T^{4} - T^{6} + T^{8} - T^{10} + T^{12} )^{4} \))(\( ( 1 - T^{2} + T^{4} - T^{6} + T^{8} - T^{10} + T^{12} )^{4} \))
$59$ (\( ( 1 + T^{2} )^{2} \))(\( ( 1 + T^{2} )^{2} \))(\( ( 1 + T^{2} )^{4} \))(\( ( 1 + T^{2} )^{4} \))(\( ( 1 - T^{2} + T^{4} - T^{6} + T^{8} - T^{10} + T^{12} )^{2} \))(\( ( 1 - T^{2} + T^{4} - T^{6} + T^{8} - T^{10} + T^{12} )^{2} \))(\( ( 1 - T^{2} + T^{4} - T^{6} + T^{8} - T^{10} + T^{12} )^{4} \))(\( ( 1 - T^{2} + T^{4} - T^{6} + T^{8} - T^{10} + T^{12} )^{4} \))
$61$ (\( 1 + T^{4} \))(\( 1 + T^{4} \))(\( ( 1 + T^{4} )^{2} \))(\( ( 1 + T^{4} )^{2} \))(\( 1 - T^{4} + T^{8} - T^{12} + T^{16} - T^{20} + T^{24} \))(\( 1 - T^{4} + T^{8} - T^{12} + T^{16} - T^{20} + T^{24} \))(\( ( 1 - T^{4} + T^{8} - T^{12} + T^{16} - T^{20} + T^{24} )^{2} \))(\( ( 1 - T^{4} + T^{8} - T^{12} + T^{16} - T^{20} + T^{24} )^{2} \))
$67$ (\( ( 1 + T^{2} )^{2} \))(\( ( 1 + T^{2} )^{2} \))(\( ( 1 + T^{2} )^{4} \))(\( ( 1 + T^{2} )^{4} \))(\( ( 1 - T^{2} + T^{4} - T^{6} + T^{8} - T^{10} + T^{12} )^{2} \))(\( ( 1 - T^{2} + T^{4} - T^{6} + T^{8} - T^{10} + T^{12} )^{2} \))(\( ( 1 - T^{2} + T^{4} - T^{6} + T^{8} - T^{10} + T^{12} )^{4} \))(\( ( 1 - T^{2} + T^{4} - T^{6} + T^{8} - T^{10} + T^{12} )^{4} \))
$71$ (\( ( 1 + T^{2} )^{2} \))(\( ( 1 + T^{2} )^{2} \))(\( ( 1 - T^{2} + T^{4} )^{2} \))(\( ( 1 - T^{2} + T^{4} )^{2} \))(\( ( 1 - T^{2} + T^{4} - T^{6} + T^{8} - T^{10} + T^{12} )^{2} \))(\( ( 1 - T^{2} + T^{4} - T^{6} + T^{8} - T^{10} + T^{12} )^{2} \))(\( ( 1 + T^{2} - T^{6} - T^{8} + T^{12} - T^{16} - T^{18} + T^{22} + T^{24} )^{2} \))(\( ( 1 + T^{2} - T^{6} - T^{8} + T^{12} - T^{16} - T^{18} + T^{22} + T^{24} )^{2} \))
$73$ (\( ( 1 + T )^{2}( 1 + T^{2} ) \))(\( ( 1 + T )^{2}( 1 + T^{2} ) \))(\( ( 1 - T + T^{2} )^{2}( 1 - T^{2} + T^{4} ) \))(\( ( 1 - T + T^{2} )^{2}( 1 - T^{2} + T^{4} ) \))(\( ( 1 - T + T^{2} - T^{3} + T^{4} - T^{5} + T^{6} )^{2}( 1 - T^{2} + T^{4} - T^{6} + T^{8} - T^{10} + T^{12} ) \))(\( ( 1 - T + T^{2} - T^{3} + T^{4} - T^{5} + T^{6} )^{2}( 1 - T^{2} + T^{4} - T^{6} + T^{8} - T^{10} + T^{12} ) \))(\( ( 1 + T - T^{3} - T^{4} + T^{6} - T^{8} - T^{9} + T^{11} + T^{12} )^{2}( 1 + T^{2} - T^{6} - T^{8} + T^{12} - T^{16} - T^{18} + T^{22} + T^{24} ) \))(\( ( 1 + T - T^{3} - T^{4} + T^{6} - T^{8} - T^{9} + T^{11} + T^{12} )^{2}( 1 + T^{2} - T^{6} - T^{8} + T^{12} - T^{16} - T^{18} + T^{22} + T^{24} ) \))
$79$ (\( 1 + T^{4} \))(\( 1 + T^{4} \))(\( ( 1 + T^{4} )^{2} \))(\( ( 1 + T^{4} )^{2} \))(\( 1 - T^{4} + T^{8} - T^{12} + T^{16} - T^{20} + T^{24} \))(\( 1 - T^{4} + T^{8} - T^{12} + T^{16} - T^{20} + T^{24} \))(\( ( 1 - T^{4} + T^{8} - T^{12} + T^{16} - T^{20} + T^{24} )^{2} \))(\( ( 1 - T^{4} + T^{8} - T^{12} + T^{16} - T^{20} + T^{24} )^{2} \))
$83$ (\( ( 1 + T^{2} )^{2} \))(\( ( 1 + T^{2} )^{2} \))(\( ( 1 + T^{2} )^{4} \))(\( ( 1 + T^{2} )^{4} \))(\( ( 1 - T^{2} + T^{4} - T^{6} + T^{8} - T^{10} + T^{12} )^{2} \))(\( ( 1 - T^{2} + T^{4} - T^{6} + T^{8} - T^{10} + T^{12} )^{2} \))(\( ( 1 - T^{2} + T^{4} - T^{6} + T^{8} - T^{10} + T^{12} )^{4} \))(\( ( 1 - T^{2} + T^{4} - T^{6} + T^{8} - T^{10} + T^{12} )^{4} \))
$89$ (\( 1 + T^{4} \))(\( 1 + T^{4} \))(\( ( 1 + T^{4} )^{2} \))(\( ( 1 + T^{4} )^{2} \))(\( 1 - T^{4} + T^{8} - T^{12} + T^{16} - T^{20} + T^{24} \))(\( 1 - T^{4} + T^{8} - T^{12} + T^{16} - T^{20} + T^{24} \))(\( ( 1 - T^{4} + T^{8} - T^{12} + T^{16} - T^{20} + T^{24} )^{2} \))(\( ( 1 - T^{4} + T^{8} - T^{12} + T^{16} - T^{20} + T^{24} )^{2} \))
$97$ (\( 1 + T^{4} \))(\( 1 + T^{4} \))(\( ( 1 + T^{4} )^{2} \))(\( ( 1 + T^{4} )^{2} \))(\( 1 - T^{4} + T^{8} - T^{12} + T^{16} - T^{20} + T^{24} \))(\( 1 - T^{4} + T^{8} - T^{12} + T^{16} - T^{20} + T^{24} \))(\( ( 1 - T^{4} + T^{8} - T^{12} + T^{16} - T^{20} + T^{24} )^{2} \))(\( ( 1 - T^{4} + T^{8} - T^{12} + T^{16} - T^{20} + T^{24} )^{2} \))
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