Properties

Label 2005.2.a
Level 2005
Weight 2
Character orbit a
Rep. character \(\chi_{2005}(1,\cdot)\)
Character field \(\Q\)
Dimension 133
Newforms 7
Sturm bound 402
Trace bound 11

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Defining parameters

Level: \( N \) = \( 2005 = 5 \cdot 401 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 2005.a (trivial)
Character field: \(\Q\)
Newforms: \( 7 \)
Sturm bound: \(402\)
Trace bound: \(11\)
Distinguishing \(T_p\): \(2\), \(11\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_0(2005))\).

Total New Old
Modular forms 202 133 69
Cusp forms 199 133 66
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.

\(5\)\(401\)FrickeDim.
\(+\)\(+\)\(+\)\(29\)
\(+\)\(-\)\(-\)\(37\)
\(-\)\(+\)\(-\)\(37\)
\(-\)\(-\)\(+\)\(30\)
Plus space\(+\)\(59\)
Minus space\(-\)\(74\)

Trace form

\(133q \) \(\mathstrut +\mathstrut 3q^{2} \) \(\mathstrut +\mathstrut 131q^{4} \) \(\mathstrut +\mathstrut q^{5} \) \(\mathstrut -\mathstrut 4q^{6} \) \(\mathstrut -\mathstrut 4q^{7} \) \(\mathstrut +\mathstrut 3q^{8} \) \(\mathstrut +\mathstrut 141q^{9} \) \(\mathstrut +\mathstrut O(q^{10}) \) \(133q \) \(\mathstrut +\mathstrut 3q^{2} \) \(\mathstrut +\mathstrut 131q^{4} \) \(\mathstrut +\mathstrut q^{5} \) \(\mathstrut -\mathstrut 4q^{6} \) \(\mathstrut -\mathstrut 4q^{7} \) \(\mathstrut +\mathstrut 3q^{8} \) \(\mathstrut +\mathstrut 141q^{9} \) \(\mathstrut -\mathstrut q^{10} \) \(\mathstrut +\mathstrut 12q^{11} \) \(\mathstrut +\mathstrut 4q^{12} \) \(\mathstrut -\mathstrut 10q^{13} \) \(\mathstrut +\mathstrut 16q^{14} \) \(\mathstrut +\mathstrut 139q^{16} \) \(\mathstrut -\mathstrut 2q^{17} \) \(\mathstrut +\mathstrut 11q^{18} \) \(\mathstrut -\mathstrut 4q^{19} \) \(\mathstrut +\mathstrut 7q^{20} \) \(\mathstrut +\mathstrut 4q^{22} \) \(\mathstrut +\mathstrut 8q^{23} \) \(\mathstrut -\mathstrut 16q^{24} \) \(\mathstrut +\mathstrut 133q^{25} \) \(\mathstrut -\mathstrut 2q^{26} \) \(\mathstrut -\mathstrut 12q^{27} \) \(\mathstrut -\mathstrut 8q^{28} \) \(\mathstrut +\mathstrut 2q^{29} \) \(\mathstrut -\mathstrut 8q^{30} \) \(\mathstrut -\mathstrut 20q^{31} \) \(\mathstrut +\mathstrut 19q^{32} \) \(\mathstrut +\mathstrut 4q^{33} \) \(\mathstrut -\mathstrut 34q^{34} \) \(\mathstrut +\mathstrut 4q^{35} \) \(\mathstrut +\mathstrut 119q^{36} \) \(\mathstrut -\mathstrut 22q^{37} \) \(\mathstrut -\mathstrut 28q^{38} \) \(\mathstrut -\mathstrut 36q^{39} \) \(\mathstrut -\mathstrut 9q^{40} \) \(\mathstrut +\mathstrut 18q^{41} \) \(\mathstrut -\mathstrut 76q^{42} \) \(\mathstrut -\mathstrut 16q^{43} \) \(\mathstrut +\mathstrut 4q^{44} \) \(\mathstrut +\mathstrut 5q^{45} \) \(\mathstrut +\mathstrut 20q^{46} \) \(\mathstrut -\mathstrut 4q^{47} \) \(\mathstrut -\mathstrut 24q^{48} \) \(\mathstrut +\mathstrut 109q^{49} \) \(\mathstrut +\mathstrut 3q^{50} \) \(\mathstrut +\mathstrut 32q^{51} \) \(\mathstrut -\mathstrut 50q^{52} \) \(\mathstrut -\mathstrut 18q^{53} \) \(\mathstrut -\mathstrut 40q^{54} \) \(\mathstrut +\mathstrut 4q^{55} \) \(\mathstrut +\mathstrut 56q^{56} \) \(\mathstrut -\mathstrut 16q^{57} \) \(\mathstrut +\mathstrut 22q^{58} \) \(\mathstrut -\mathstrut 8q^{59} \) \(\mathstrut +\mathstrut 16q^{60} \) \(\mathstrut -\mathstrut 22q^{61} \) \(\mathstrut -\mathstrut 36q^{62} \) \(\mathstrut -\mathstrut 16q^{63} \) \(\mathstrut +\mathstrut 131q^{64} \) \(\mathstrut +\mathstrut 6q^{65} \) \(\mathstrut +\mathstrut 16q^{66} \) \(\mathstrut -\mathstrut 4q^{67} \) \(\mathstrut +\mathstrut 62q^{68} \) \(\mathstrut -\mathstrut 72q^{69} \) \(\mathstrut +\mathstrut 24q^{70} \) \(\mathstrut +\mathstrut 4q^{71} \) \(\mathstrut +\mathstrut 43q^{72} \) \(\mathstrut -\mathstrut 14q^{73} \) \(\mathstrut +\mathstrut 38q^{74} \) \(\mathstrut +\mathstrut 32q^{76} \) \(\mathstrut -\mathstrut 24q^{77} \) \(\mathstrut +\mathstrut 20q^{78} \) \(\mathstrut +\mathstrut 36q^{79} \) \(\mathstrut -\mathstrut q^{80} \) \(\mathstrut +\mathstrut 197q^{81} \) \(\mathstrut +\mathstrut 26q^{82} \) \(\mathstrut +\mathstrut 40q^{83} \) \(\mathstrut +\mathstrut 8q^{84} \) \(\mathstrut -\mathstrut 6q^{85} \) \(\mathstrut +\mathstrut 64q^{86} \) \(\mathstrut -\mathstrut 40q^{87} \) \(\mathstrut +\mathstrut 40q^{88} \) \(\mathstrut +\mathstrut 18q^{89} \) \(\mathstrut -\mathstrut 29q^{90} \) \(\mathstrut -\mathstrut 36q^{91} \) \(\mathstrut +\mathstrut 52q^{92} \) \(\mathstrut -\mathstrut 28q^{93} \) \(\mathstrut -\mathstrut 48q^{94} \) \(\mathstrut -\mathstrut 12q^{95} \) \(\mathstrut +\mathstrut 32q^{96} \) \(\mathstrut +\mathstrut 10q^{97} \) \(\mathstrut +\mathstrut 27q^{98} \) \(\mathstrut +\mathstrut 56q^{99} \) \(\mathstrut +\mathstrut O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(2005))\) into irreducible Hecke orbits

Label Dim. \(A\) Field CM Traces A-L signs $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\) 5 401
2005.2.a.a \(1\) \(16.010\) \(\Q\) None \(-1\) \(0\) \(1\) \(0\) \(-\) \(-\) \(q-q^{2}-q^{4}+q^{5}+3q^{8}-3q^{9}-q^{10}+\cdots\)
2005.2.a.b \(1\) \(16.010\) \(\Q\) None \(-1\) \(0\) \(1\) \(0\) \(-\) \(-\) \(q-q^{2}-q^{4}+q^{5}+3q^{8}-3q^{9}-q^{10}+\cdots\)
2005.2.a.c \(3\) \(16.010\) \(\Q(\zeta_{18})^+\) None \(-3\) \(-3\) \(3\) \(-3\) \(-\) \(-\) \(q+(-1+\beta _{1})q^{2}+(-1-2\beta _{1}+\beta _{2})q^{3}+\cdots\)
2005.2.a.d \(25\) \(16.010\) None \(-5\) \(-10\) \(25\) \(-31\) \(-\) \(-\)
2005.2.a.e \(29\) \(16.010\) None \(-5\) \(-3\) \(-29\) \(12\) \(+\) \(+\)
2005.2.a.f \(37\) \(16.010\) None \(7\) \(3\) \(-37\) \(-16\) \(+\) \(-\)
2005.2.a.g \(37\) \(16.010\) None \(11\) \(13\) \(37\) \(34\) \(-\) \(+\)

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_0(2005))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_0(2005)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_0(401))\)\(^{\oplus 2}\)