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Properties

Label 2007.1
Level 2007
Weight 1
Dimension 46
Nonzero newspaces 2
Newform subspaces 4
Sturm bound 298368
Trace bound 1

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Defining parameters

Level: \( N \) = \( 2007 = 3^{2} \cdot 223 \)
Weight: \( k \) = \( 1 \)
Nonzero newspaces: \( 2 \)
Newform subspaces: \( 4 \)
Sturm bound: \(298368\)
Trace bound: \(1\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{1}(\Gamma_1(2007))\).

Total New Old
Modular forms 1903 1041 862
Cusp forms 127 46 81
Eisenstein series 1776 995 781

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

\(D_n\) \(A_4\) \(S_4\) \(A_5\)
Dimension 46 0 0 0

Trace form

\( 46 q + q^{2} + 10 q^{4} + q^{7} + 2 q^{8} + O(q^{10}) \) \( 46 q + q^{2} + 10 q^{4} + q^{7} + 2 q^{8} + 2 q^{14} + 7 q^{16} + q^{17} - 3 q^{19} + 9 q^{25} - 5 q^{28} + q^{29} + q^{31} + 3 q^{32} - 2 q^{34} - 3 q^{37} + 2 q^{38} + q^{41} - 3 q^{43} + q^{47} + 6 q^{49} + q^{50} + q^{53} - 3 q^{56} - 9 q^{58} - 5 q^{62} + 8 q^{64} - 4 q^{68} + q^{73} + 2 q^{74} - 8 q^{76} - 2 q^{82} + q^{83} - 5 q^{86} + q^{89} - 2 q^{94} - 4 q^{98} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{1}^{\mathrm{new}}(\Gamma_1(2007))\)

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
2007.1.b \(\chi_{2007}(224, \cdot)\) None 0 1
2007.1.d \(\chi_{2007}(1783, \cdot)\) 2007.1.d.a 1 1
2007.1.d.b 3
2007.1.d.c 6
2007.1.j \(\chi_{2007}(485, \cdot)\) None 0 2
2007.1.k \(\chi_{2007}(184, \cdot)\) None 0 2
2007.1.l \(\chi_{2007}(445, \cdot)\) None 0 2
2007.1.m \(\chi_{2007}(40, \cdot)\) None 0 2
2007.1.n \(\chi_{2007}(1298, \cdot)\) None 0 2
2007.1.q \(\chi_{2007}(1154, \cdot)\) None 0 2
2007.1.r \(\chi_{2007}(893, \cdot)\) None 0 2
2007.1.t \(\chi_{2007}(1378, \cdot)\) None 0 2
2007.1.v \(\chi_{2007}(91, \cdot)\) 2007.1.v.a 36 36
2007.1.x \(\chi_{2007}(8, \cdot)\) None 0 36
2007.1.bc \(\chi_{2007}(10, \cdot)\) None 0 72
2007.1.be \(\chi_{2007}(2, \cdot)\) None 0 72
2007.1.bf \(\chi_{2007}(38, \cdot)\) None 0 72
2007.1.bi \(\chi_{2007}(29, \cdot)\) None 0 72
2007.1.bj \(\chi_{2007}(22, \cdot)\) None 0 72
2007.1.bk \(\chi_{2007}(13, \cdot)\) None 0 72
2007.1.bl \(\chi_{2007}(67, \cdot)\) None 0 72
2007.1.bm \(\chi_{2007}(53, \cdot)\) None 0 72

Decomposition of \(S_{1}^{\mathrm{old}}(\Gamma_1(2007))\) into lower level spaces

\( S_{1}^{\mathrm{old}}(\Gamma_1(2007)) \cong \) \(S_{1}^{\mathrm{new}}(\Gamma_1(223))\)\(^{\oplus 3}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(669))\)\(^{\oplus 2}\)