Properties

Label 1005.2.g
Level 1005
Weight 2
Character orbit g
Rep. character \(\chi_{1005}(401,\cdot)\)
Character field \(\Q\)
Dimension 92
Newforms 2
Sturm bound 272
Trace bound 5

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Defining parameters

Level: \( N \) = \( 1005 = 3 \cdot 5 \cdot 67 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 1005.g (of order \(2\) and degree \(1\))
Character conductor: \(\operatorname{cond}(\chi)\) = \( 201 \)
Character field: \(\Q\)
Newforms: \( 2 \)
Sturm bound: \(272\)
Trace bound: \(5\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(1005, [\chi])\).

Total New Old
Modular forms 140 92 48
Cusp forms 132 92 40
Eisenstein series 8 0 8

Trace form

\(92q \) \(\mathstrut +\mathstrut 96q^{4} \) \(\mathstrut +\mathstrut 16q^{9} \) \(\mathstrut +\mathstrut O(q^{10}) \) \(92q \) \(\mathstrut +\mathstrut 96q^{4} \) \(\mathstrut +\mathstrut 16q^{9} \) \(\mathstrut +\mathstrut 72q^{16} \) \(\mathstrut -\mathstrut 40q^{19} \) \(\mathstrut -\mathstrut 8q^{21} \) \(\mathstrut +\mathstrut 32q^{22} \) \(\mathstrut -\mathstrut 16q^{24} \) \(\mathstrut +\mathstrut 92q^{25} \) \(\mathstrut -\mathstrut 40q^{33} \) \(\mathstrut +\mathstrut 56q^{36} \) \(\mathstrut -\mathstrut 32q^{37} \) \(\mathstrut +\mathstrut 24q^{39} \) \(\mathstrut -\mathstrut 44q^{49} \) \(\mathstrut -\mathstrut 16q^{54} \) \(\mathstrut +\mathstrut 16q^{55} \) \(\mathstrut +\mathstrut 32q^{64} \) \(\mathstrut -\mathstrut 56q^{67} \) \(\mathstrut +\mathstrut 16q^{73} \) \(\mathstrut -\mathstrut 128q^{76} \) \(\mathstrut +\mathstrut 40q^{81} \) \(\mathstrut -\mathstrut 24q^{82} \) \(\mathstrut -\mathstrut 34q^{84} \) \(\mathstrut +\mathstrut 8q^{88} \) \(\mathstrut -\mathstrut 18q^{90} \) \(\mathstrut +\mathstrut 56q^{91} \) \(\mathstrut +\mathstrut 4q^{93} \) \(\mathstrut -\mathstrut 98q^{96} \) \(\mathstrut +\mathstrut O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(1005, [\chi])\) into irreducible Hecke orbits

Label Dim. \(A\) Field CM Traces $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\)
1005.2.g.a \(46\) \(8.025\) None \(0\) \(0\) \(-46\) \(0\)
1005.2.g.b \(46\) \(8.025\) None \(0\) \(0\) \(46\) \(0\)

Decomposition of \(S_{2}^{\mathrm{old}}(1005, [\chi])\) into lower level spaces

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