Properties

Label 1006.2.a
Level 1006
Weight 2
Character orbit a
Rep. character \(\chi_{1006}(1,\cdot)\)
Character field \(\Q\)
Dimension 41
Newforms 10
Sturm bound 252
Trace bound 3

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Defining parameters

Level: \( N \) = \( 1006 = 2 \cdot 503 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 1006.a (trivial)
Character field: \(\Q\)
Newforms: \( 10 \)
Sturm bound: \(252\)
Trace bound: \(3\)
Distinguishing \(T_p\): \(3\), \(5\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_0(1006))\).

Total New Old
Modular forms 128 41 87
Cusp forms 125 41 84
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.

\(2\)\(503\)FrickeDim.
\(+\)\(+\)\(+\)\(8\)
\(+\)\(-\)\(-\)\(13\)
\(-\)\(+\)\(-\)\(12\)
\(-\)\(-\)\(+\)\(8\)
Plus space\(+\)\(16\)
Minus space\(-\)\(25\)

Trace form

\(41q \) \(\mathstrut -\mathstrut q^{2} \) \(\mathstrut -\mathstrut 4q^{3} \) \(\mathstrut +\mathstrut 41q^{4} \) \(\mathstrut -\mathstrut 4q^{7} \) \(\mathstrut -\mathstrut q^{8} \) \(\mathstrut +\mathstrut 41q^{9} \) \(\mathstrut +\mathstrut O(q^{10}) \) \(41q \) \(\mathstrut -\mathstrut q^{2} \) \(\mathstrut -\mathstrut 4q^{3} \) \(\mathstrut +\mathstrut 41q^{4} \) \(\mathstrut -\mathstrut 4q^{7} \) \(\mathstrut -\mathstrut q^{8} \) \(\mathstrut +\mathstrut 41q^{9} \) \(\mathstrut -\mathstrut 4q^{10} \) \(\mathstrut +\mathstrut 4q^{11} \) \(\mathstrut -\mathstrut 4q^{12} \) \(\mathstrut -\mathstrut 6q^{13} \) \(\mathstrut -\mathstrut 8q^{15} \) \(\mathstrut +\mathstrut 41q^{16} \) \(\mathstrut -\mathstrut 10q^{17} \) \(\mathstrut -\mathstrut 5q^{18} \) \(\mathstrut -\mathstrut 6q^{19} \) \(\mathstrut -\mathstrut 8q^{21} \) \(\mathstrut -\mathstrut 12q^{22} \) \(\mathstrut -\mathstrut 20q^{23} \) \(\mathstrut +\mathstrut 23q^{25} \) \(\mathstrut -\mathstrut 2q^{26} \) \(\mathstrut -\mathstrut 28q^{27} \) \(\mathstrut -\mathstrut 4q^{28} \) \(\mathstrut +\mathstrut 8q^{29} \) \(\mathstrut -\mathstrut 4q^{30} \) \(\mathstrut -\mathstrut 8q^{31} \) \(\mathstrut -\mathstrut q^{32} \) \(\mathstrut -\mathstrut 6q^{34} \) \(\mathstrut -\mathstrut 4q^{35} \) \(\mathstrut +\mathstrut 41q^{36} \) \(\mathstrut -\mathstrut 16q^{37} \) \(\mathstrut +\mathstrut 10q^{38} \) \(\mathstrut -\mathstrut 8q^{39} \) \(\mathstrut -\mathstrut 4q^{40} \) \(\mathstrut +\mathstrut 2q^{41} \) \(\mathstrut +\mathstrut 4q^{42} \) \(\mathstrut +\mathstrut 4q^{43} \) \(\mathstrut +\mathstrut 4q^{44} \) \(\mathstrut +\mathstrut 4q^{46} \) \(\mathstrut +\mathstrut 24q^{47} \) \(\mathstrut -\mathstrut 4q^{48} \) \(\mathstrut +\mathstrut 53q^{49} \) \(\mathstrut -\mathstrut 7q^{50} \) \(\mathstrut +\mathstrut 8q^{51} \) \(\mathstrut -\mathstrut 6q^{52} \) \(\mathstrut +\mathstrut 4q^{53} \) \(\mathstrut +\mathstrut 12q^{54} \) \(\mathstrut +\mathstrut 16q^{55} \) \(\mathstrut +\mathstrut 20q^{57} \) \(\mathstrut -\mathstrut 20q^{58} \) \(\mathstrut +\mathstrut 12q^{59} \) \(\mathstrut -\mathstrut 8q^{60} \) \(\mathstrut -\mathstrut 2q^{61} \) \(\mathstrut -\mathstrut 4q^{62} \) \(\mathstrut +\mathstrut 8q^{63} \) \(\mathstrut +\mathstrut 41q^{64} \) \(\mathstrut +\mathstrut 44q^{65} \) \(\mathstrut +\mathstrut 24q^{66} \) \(\mathstrut -\mathstrut 24q^{67} \) \(\mathstrut -\mathstrut 10q^{68} \) \(\mathstrut +\mathstrut 40q^{69} \) \(\mathstrut -\mathstrut 24q^{70} \) \(\mathstrut +\mathstrut 12q^{71} \) \(\mathstrut -\mathstrut 5q^{72} \) \(\mathstrut -\mathstrut 14q^{73} \) \(\mathstrut +\mathstrut 16q^{74} \) \(\mathstrut -\mathstrut 56q^{75} \) \(\mathstrut -\mathstrut 6q^{76} \) \(\mathstrut +\mathstrut 4q^{77} \) \(\mathstrut +\mathstrut 4q^{78} \) \(\mathstrut +\mathstrut 4q^{79} \) \(\mathstrut +\mathstrut 9q^{81} \) \(\mathstrut -\mathstrut 30q^{82} \) \(\mathstrut +\mathstrut 40q^{83} \) \(\mathstrut -\mathstrut 8q^{84} \) \(\mathstrut -\mathstrut 16q^{85} \) \(\mathstrut -\mathstrut 20q^{86} \) \(\mathstrut -\mathstrut 8q^{87} \) \(\mathstrut -\mathstrut 12q^{88} \) \(\mathstrut +\mathstrut 2q^{89} \) \(\mathstrut +\mathstrut 8q^{90} \) \(\mathstrut -\mathstrut 28q^{91} \) \(\mathstrut -\mathstrut 20q^{92} \) \(\mathstrut +\mathstrut 24q^{93} \) \(\mathstrut +\mathstrut 4q^{94} \) \(\mathstrut -\mathstrut 36q^{95} \) \(\mathstrut -\mathstrut 66q^{97} \) \(\mathstrut +\mathstrut 7q^{98} \) \(\mathstrut +\mathstrut 60q^{99} \) \(\mathstrut +\mathstrut O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(1006))\) into irreducible Hecke orbits

Label Dim. \(A\) Field CM Traces A-L signs $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\) 2 503
1006.2.a.a \(1\) \(8.033\) \(\Q\) None \(-1\) \(0\) \(0\) \(0\) \(+\) \(-\) \(q-q^{2}+q^{4}-q^{8}-3q^{9}+4q^{11}+2q^{13}+\cdots\)
1006.2.a.b \(1\) \(8.033\) \(\Q\) None \(-1\) \(1\) \(-2\) \(1\) \(+\) \(+\) \(q-q^{2}+q^{3}+q^{4}-2q^{5}-q^{6}+q^{7}+\cdots\)
1006.2.a.c \(1\) \(8.033\) \(\Q\) None \(1\) \(-3\) \(0\) \(-3\) \(-\) \(-\) \(q+q^{2}-3q^{3}+q^{4}-3q^{6}-3q^{7}+q^{8}+\cdots\)
1006.2.a.d \(1\) \(8.033\) \(\Q\) None \(1\) \(-1\) \(0\) \(1\) \(-\) \(-\) \(q+q^{2}-q^{3}+q^{4}-q^{6}+q^{7}+q^{8}+\cdots\)
1006.2.a.e \(1\) \(8.033\) \(\Q\) None \(1\) \(1\) \(-4\) \(1\) \(-\) \(-\) \(q+q^{2}+q^{3}+q^{4}-4q^{5}+q^{6}+q^{7}+\cdots\)
1006.2.a.f \(2\) \(8.033\) \(\Q(\sqrt{5}) \) None \(-2\) \(0\) \(-2\) \(-4\) \(+\) \(+\) \(q-q^{2}-\beta q^{3}+q^{4}+(-1-\beta )q^{5}+\beta q^{6}+\cdots\)
1006.2.a.g \(5\) \(8.033\) 5.5.36497.1 None \(-5\) \(0\) \(-1\) \(3\) \(+\) \(+\) \(q-q^{2}+(\beta _{1}-\beta _{3}+\beta _{4})q^{3}+q^{4}+(\beta _{2}+\cdots)q^{5}+\cdots\)
1006.2.a.h \(5\) \(8.033\) 5.5.205225.1 None \(5\) \(-4\) \(-3\) \(-9\) \(-\) \(-\) \(q+q^{2}+(-1+\beta _{1})q^{3}+q^{4}+(-1-\beta _{1}+\cdots)q^{5}+\cdots\)
1006.2.a.i \(12\) \(8.033\) \(\mathbb{Q}[x]/(x^{12} - \cdots)\) None \(-12\) \(-3\) \(7\) \(-2\) \(+\) \(-\) \(q-q^{2}-\beta _{4}q^{3}+q^{4}+(\beta _{7}-\beta _{10})q^{5}+\cdots\)
1006.2.a.j \(12\) \(8.033\) \(\mathbb{Q}[x]/(x^{12} - \cdots)\) None \(12\) \(5\) \(5\) \(8\) \(-\) \(+\) \(q+q^{2}+\beta _{1}q^{3}+q^{4}-\beta _{9}q^{5}+\beta _{1}q^{6}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_0(1006))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_0(1006)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_0(503))\)\(^{\oplus 2}\)