Properties

Label 4006.2.a
Level 4006
Weight 2
Character orbit a
Rep. character \(\chi_{4006}(1,\cdot)\)
Character field \(\Q\)
Dimension 166
Newforms 9
Sturm bound 1002
Trace bound 3

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Defining parameters

Level: \( N \) = \( 4006 = 2 \cdot 2003 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 4006.a (trivial)
Character field: \(\Q\)
Newforms: \( 9 \)
Sturm bound: \(1002\)
Trace bound: \(3\)
Distinguishing \(T_p\): \(3\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_0(4006))\).

Total New Old
Modular forms 503 166 337
Cusp forms 500 166 334
Eisenstein series 3 0 3

The following table gives the dimensions of the cuspidal new subspaces with specified eigenvalues for the Atkin-Lehner operators and the Fricke involution.

\(2\)\(2003\)FrickeDim.
\(+\)\(+\)\(+\)\(40\)
\(+\)\(-\)\(-\)\(43\)
\(-\)\(+\)\(-\)\(47\)
\(-\)\(-\)\(+\)\(36\)
Plus space\(+\)\(76\)
Minus space\(-\)\(90\)

Trace form

\(166q \) \(\mathstrut +\mathstrut 2q^{3} \) \(\mathstrut +\mathstrut 166q^{4} \) \(\mathstrut +\mathstrut 4q^{6} \) \(\mathstrut -\mathstrut 4q^{7} \) \(\mathstrut +\mathstrut 164q^{9} \) \(\mathstrut +\mathstrut O(q^{10}) \) \(166q \) \(\mathstrut +\mathstrut 2q^{3} \) \(\mathstrut +\mathstrut 166q^{4} \) \(\mathstrut +\mathstrut 4q^{6} \) \(\mathstrut -\mathstrut 4q^{7} \) \(\mathstrut +\mathstrut 164q^{9} \) \(\mathstrut -\mathstrut 2q^{10} \) \(\mathstrut -\mathstrut 4q^{11} \) \(\mathstrut +\mathstrut 2q^{12} \) \(\mathstrut -\mathstrut 2q^{13} \) \(\mathstrut -\mathstrut 4q^{14} \) \(\mathstrut -\mathstrut 4q^{15} \) \(\mathstrut +\mathstrut 166q^{16} \) \(\mathstrut -\mathstrut 4q^{17} \) \(\mathstrut -\mathstrut 2q^{19} \) \(\mathstrut +\mathstrut 6q^{22} \) \(\mathstrut +\mathstrut 8q^{23} \) \(\mathstrut +\mathstrut 4q^{24} \) \(\mathstrut +\mathstrut 176q^{25} \) \(\mathstrut +\mathstrut 8q^{27} \) \(\mathstrut -\mathstrut 4q^{28} \) \(\mathstrut -\mathstrut 8q^{29} \) \(\mathstrut +\mathstrut 12q^{30} \) \(\mathstrut -\mathstrut 4q^{31} \) \(\mathstrut +\mathstrut 36q^{33} \) \(\mathstrut -\mathstrut 4q^{34} \) \(\mathstrut +\mathstrut 4q^{35} \) \(\mathstrut +\mathstrut 164q^{36} \) \(\mathstrut +\mathstrut 16q^{37} \) \(\mathstrut +\mathstrut 4q^{38} \) \(\mathstrut -\mathstrut 24q^{39} \) \(\mathstrut -\mathstrut 2q^{40} \) \(\mathstrut +\mathstrut 8q^{41} \) \(\mathstrut +\mathstrut 28q^{42} \) \(\mathstrut -\mathstrut 8q^{43} \) \(\mathstrut -\mathstrut 4q^{44} \) \(\mathstrut -\mathstrut 8q^{47} \) \(\mathstrut +\mathstrut 2q^{48} \) \(\mathstrut +\mathstrut 150q^{49} \) \(\mathstrut -\mathstrut 8q^{50} \) \(\mathstrut -\mathstrut 4q^{51} \) \(\mathstrut -\mathstrut 2q^{52} \) \(\mathstrut -\mathstrut 2q^{53} \) \(\mathstrut +\mathstrut 28q^{54} \) \(\mathstrut +\mathstrut 4q^{55} \) \(\mathstrut -\mathstrut 4q^{56} \) \(\mathstrut -\mathstrut 52q^{57} \) \(\mathstrut -\mathstrut 6q^{58} \) \(\mathstrut -\mathstrut 26q^{59} \) \(\mathstrut -\mathstrut 4q^{60} \) \(\mathstrut -\mathstrut 8q^{61} \) \(\mathstrut -\mathstrut 4q^{62} \) \(\mathstrut -\mathstrut 44q^{63} \) \(\mathstrut +\mathstrut 166q^{64} \) \(\mathstrut -\mathstrut 24q^{65} \) \(\mathstrut +\mathstrut 8q^{66} \) \(\mathstrut -\mathstrut 36q^{67} \) \(\mathstrut -\mathstrut 4q^{68} \) \(\mathstrut +\mathstrut 24q^{70} \) \(\mathstrut -\mathstrut 28q^{71} \) \(\mathstrut -\mathstrut 16q^{73} \) \(\mathstrut -\mathstrut 2q^{74} \) \(\mathstrut -\mathstrut 2q^{75} \) \(\mathstrut -\mathstrut 2q^{76} \) \(\mathstrut -\mathstrut 4q^{77} \) \(\mathstrut -\mathstrut 24q^{78} \) \(\mathstrut +\mathstrut 4q^{79} \) \(\mathstrut +\mathstrut 174q^{81} \) \(\mathstrut -\mathstrut 20q^{82} \) \(\mathstrut -\mathstrut 36q^{83} \) \(\mathstrut -\mathstrut 40q^{85} \) \(\mathstrut -\mathstrut 2q^{86} \) \(\mathstrut +\mathstrut 6q^{88} \) \(\mathstrut -\mathstrut 18q^{90} \) \(\mathstrut -\mathstrut 80q^{91} \) \(\mathstrut +\mathstrut 8q^{92} \) \(\mathstrut +\mathstrut 8q^{93} \) \(\mathstrut +\mathstrut 4q^{94} \) \(\mathstrut -\mathstrut 4q^{95} \) \(\mathstrut +\mathstrut 4q^{96} \) \(\mathstrut -\mathstrut 20q^{97} \) \(\mathstrut -\mathstrut 16q^{98} \) \(\mathstrut +\mathstrut 24q^{99} \) \(\mathstrut +\mathstrut O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(4006))\) into irreducible Hecke orbits

Label Dim. \(A\) Field CM Traces A-L signs $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\) 2 2003
4006.2.a.a \(1\) \(31.988\) \(\Q\) None \(-1\) \(0\) \(-3\) \(-2\) \(+\) \(-\) \(q-q^{2}+q^{4}-3q^{5}-2q^{7}-q^{8}-3q^{9}+\cdots\)
4006.2.a.b \(1\) \(31.988\) \(\Q\) None \(1\) \(-2\) \(-3\) \(-2\) \(-\) \(+\) \(q+q^{2}-2q^{3}+q^{4}-3q^{5}-2q^{6}-2q^{7}+\cdots\)
4006.2.a.c \(1\) \(31.988\) \(\Q\) None \(1\) \(1\) \(2\) \(-2\) \(-\) \(-\) \(q+q^{2}+q^{3}+q^{4}+2q^{5}+q^{6}-2q^{7}+\cdots\)
4006.2.a.d \(2\) \(31.988\) \(\Q(\sqrt{2}) \) None \(2\) \(-4\) \(2\) \(-4\) \(-\) \(-\) \(q+q^{2}+(-2+\beta )q^{3}+q^{4}+q^{5}+(-2+\cdots)q^{6}+\cdots\)
4006.2.a.e \(2\) \(31.988\) \(\Q(\sqrt{2}) \) None \(2\) \(0\) \(-2\) \(-4\) \(-\) \(-\) \(q+q^{2}+\beta q^{3}+q^{4}-q^{5}+\beta q^{6}+(-2+\cdots)q^{7}+\cdots\)
4006.2.a.f \(31\) \(31.988\) None \(31\) \(-13\) \(-23\) \(-18\) \(-\) \(-\)
4006.2.a.g \(40\) \(31.988\) None \(-40\) \(-1\) \(-23\) \(12\) \(+\) \(+\)
4006.2.a.h \(42\) \(31.988\) None \(-42\) \(0\) \(27\) \(-10\) \(+\) \(-\)
4006.2.a.i \(46\) \(31.988\) None \(46\) \(21\) \(23\) \(26\) \(-\) \(+\)

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_0(4006))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_0(4006)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_0(2003))\)\(^{\oplus 2}\)