Properties

Label 2010.2.d
Level 2010
Weight 2
Character orbit d
Rep. character \(\chi_{2010}(401,\cdot)\)
Character field \(\Q\)
Dimension 88
Newforms 6
Sturm bound 816
Trace bound 2

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Defining parameters

Level: \( N \) = \( 2010 = 2 \cdot 3 \cdot 5 \cdot 67 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 2010.d (of order \(2\) and degree \(1\))
Character conductor: \(\operatorname{cond}(\chi)\) = \( 201 \)
Character field: \(\Q\)
Newforms: \( 6 \)
Sturm bound: \(816\)
Trace bound: \(2\)
Distinguishing \(T_p\): \(7\), \(11\), \(53\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(2010, [\chi])\).

Total New Old
Modular forms 416 88 328
Cusp forms 400 88 312
Eisenstein series 16 0 16

Trace form

\( 88q + 88q^{4} - 8q^{9} + O(q^{10}) \) \( 88q + 88q^{4} - 8q^{9} + 88q^{16} + 48q^{19} + 24q^{22} + 88q^{25} + 8q^{33} - 8q^{36} + 40q^{37} - 24q^{39} - 104q^{49} - 24q^{55} + 88q^{64} + 48q^{67} + 48q^{73} + 48q^{76} + 24q^{81} + 24q^{82} + 24q^{88} + 16q^{91} - 8q^{93} + O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(2010, [\chi])\) into irreducible Hecke orbits

Label Dim. \(A\) Field CM Traces $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\)
2010.2.d.a \(2\) \(16.050\) \(\Q(\sqrt{-2}) \) None \(-2\) \(-2\) \(-2\) \(0\) \(q-q^{2}+(-1-\beta )q^{3}+q^{4}-q^{5}+(1+\cdots)q^{6}+\cdots\)
2010.2.d.b \(2\) \(16.050\) \(\Q(\sqrt{-2}) \) None \(2\) \(2\) \(2\) \(0\) \(q+q^{2}+(1-\beta )q^{3}+q^{4}+q^{5}+(1-\beta )q^{6}+\cdots\)
2010.2.d.c \(20\) \(16.050\) \(\mathbb{Q}[x]/(x^{20} - \cdots)\) None \(-20\) \(2\) \(-20\) \(0\) \(q-q^{2}+\beta _{1}q^{3}+q^{4}-q^{5}-\beta _{1}q^{6}+\cdots\)
2010.2.d.d \(20\) \(16.050\) \(\mathbb{Q}[x]/(x^{20} - \cdots)\) None \(20\) \(-2\) \(20\) \(0\) \(q+q^{2}+\beta _{4}q^{3}+q^{4}+q^{5}+\beta _{4}q^{6}+\cdots\)
2010.2.d.e \(22\) \(16.050\) None \(-22\) \(0\) \(22\) \(0\)
2010.2.d.f \(22\) \(16.050\) None \(22\) \(0\) \(-22\) \(0\)

Decomposition of \(S_{2}^{\mathrm{old}}(2010, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(2010, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(201, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(402, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(1005, [\chi])\)\(^{\oplus 2}\)