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

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

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

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