Properties

Label 4014.2.d
Level 4014
Weight 2
Character orbit d
Rep. character \(\chi_{4014}(4013,\cdot)\)
Character field \(\Q\)
Dimension 72
Newforms 1
Sturm bound 1344
Trace bound 0

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Defining parameters

Level: \( N \) = \( 4014 = 2 \cdot 3^{2} \cdot 223 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 4014.d (of order \(2\) and degree \(1\))
Character conductor: \(\operatorname{cond}(\chi)\) = \( 669 \)
Character field: \(\Q\)
Newforms: \( 1 \)
Sturm bound: \(1344\)
Trace bound: \(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(4014, [\chi])\).

Total New Old
Modular forms 680 72 608
Cusp forms 664 72 592
Eisenstein series 16 0 16

Trace form

\(72q \) \(\mathstrut -\mathstrut 72q^{4} \) \(\mathstrut +\mathstrut 16q^{7} \) \(\mathstrut +\mathstrut O(q^{10}) \) \(72q \) \(\mathstrut -\mathstrut 72q^{4} \) \(\mathstrut +\mathstrut 16q^{7} \) \(\mathstrut +\mathstrut 72q^{16} \) \(\mathstrut -\mathstrut 40q^{19} \) \(\mathstrut +\mathstrut 96q^{25} \) \(\mathstrut -\mathstrut 16q^{28} \) \(\mathstrut -\mathstrut 24q^{37} \) \(\mathstrut -\mathstrut 8q^{43} \) \(\mathstrut +\mathstrut 56q^{49} \) \(\mathstrut +\mathstrut 40q^{58} \) \(\mathstrut -\mathstrut 72q^{64} \) \(\mathstrut -\mathstrut 32q^{73} \) \(\mathstrut +\mathstrut 40q^{76} \) \(\mathstrut +\mathstrut 16q^{82} \) \(\mathstrut +\mathstrut O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(4014, [\chi])\) into irreducible Hecke orbits

Label Dim. \(A\) Field CM Traces $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\)
4014.2.d.a \(72\) \(32.052\) None \(0\) \(0\) \(0\) \(16\)

Decomposition of \(S_{2}^{\mathrm{old}}(4014, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(4014, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(669, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(1338, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(2007, [\chi])\)\(^{\oplus 2}\)