Properties

Label 4020.2.f
Level 4020
Weight 2
Character orbit f
Rep. character \(\chi_{4020}(401,\cdot)\)
Character field \(\Q\)
Dimension 92
Newforms 2
Sturm bound 1632
Trace bound 5

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Defining parameters

Level: \( N \) = \( 4020 = 2^{2} \cdot 3 \cdot 5 \cdot 67 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 4020.f (of order \(2\) and degree \(1\))
Character conductor: \(\operatorname{cond}(\chi)\) = \( 201 \)
Character field: \(\Q\)
Newforms: \( 2 \)
Sturm bound: \(1632\)
Trace bound: \(5\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(4020, [\chi])\).

Total New Old
Modular forms 828 92 736
Cusp forms 804 92 712
Eisenstein series 24 0 24

Trace form

\(92q \) \(\mathstrut -\mathstrut 8q^{9} \) \(\mathstrut +\mathstrut O(q^{10}) \) \(92q \) \(\mathstrut -\mathstrut 8q^{9} \) \(\mathstrut +\mathstrut 16q^{19} \) \(\mathstrut +\mathstrut 92q^{25} \) \(\mathstrut +\mathstrut 8q^{33} \) \(\mathstrut -\mathstrut 16q^{37} \) \(\mathstrut -\mathstrut 24q^{39} \) \(\mathstrut -\mathstrut 124q^{49} \) \(\mathstrut -\mathstrut 28q^{67} \) \(\mathstrut -\mathstrut 80q^{73} \) \(\mathstrut -\mathstrut 24q^{81} \) \(\mathstrut -\mathstrut 8q^{91} \) \(\mathstrut +\mathstrut 4q^{93} \) \(\mathstrut +\mathstrut O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(4020, [\chi])\) into irreducible Hecke orbits

Label Dim. \(A\) Field CM Traces $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\)
4020.2.f.a \(46\) \(32.100\) None \(0\) \(0\) \(-46\) \(0\)
4020.2.f.b \(46\) \(32.100\) None \(0\) \(0\) \(46\) \(0\)

Decomposition of \(S_{2}^{\mathrm{old}}(4020, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(4020, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(201, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(402, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(804, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(1005, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(2010, [\chi])\)\(^{\oplus 2}\)