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Properties

Label 4014.2.d
Level $4014$
Weight $2$
Character orbit 4014.d
Rep. character $\chi_{4014}(4013,\cdot)$
Character field $\Q$
Dimension $72$
Newform subspaces $1$
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: \(\Q\)
Newform subspaces: \( 1 \)
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

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

Display 100 coefficients 10 coefficients

Decomposition of \(S_{2}^{\mathrm{new}}(4014, [\chi])\) into newform subspaces

Label Char Prim Dim $A$ Field CM Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
4014.2.d.a 4014.d 669.c $72$ $32.052$ None \(0\) \(0\) \(0\) \(16\) $\mathrm{SU}(2)[C_{2}]$

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

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