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Properties

Label 840.2.da
Level $840$
Weight $2$
Character orbit 840.da
Rep. character $\chi_{840}(89,\cdot)$
Character field $\Q(\zeta_{6})$
Dimension $96$
Newform subspaces $2$
Sturm bound $384$
Trace bound $3$

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Defining parameters

Level: \( N \) \(=\) \( 840 = 2^{3} \cdot 3 \cdot 5 \cdot 7 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 840.da (of order \(6\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 105 \)
Character field: \(\Q(\zeta_{6})\)
Newform subspaces: \( 2 \)
Sturm bound: \(384\)
Trace bound: \(3\)
Distinguishing \(T_p\): \(17\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(840, [\chi])\).

Total New Old
Modular forms 416 96 320
Cusp forms 352 96 256
Eisenstein series 64 0 64

Trace form

\( 96 q - 2 q^{9} + O(q^{10}) \) \( 96 q - 2 q^{9} - 8 q^{15} + 10 q^{21} + 2 q^{25} + 12 q^{31} + 4 q^{39} - 24 q^{45} + 24 q^{51} + 36 q^{61} - 54 q^{75} + 4 q^{79} - 18 q^{81} + 48 q^{91} - 24 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{2}^{\mathrm{new}}(840, [\chi])\) into newform subspaces

Label Char Prim Dim $A$ Field CM Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
840.2.da.a 840.da 105.p $48$ $6.707$ None \(0\) \(-3\) \(-3\) \(0\) $\mathrm{SU}(2)[C_{6}]$
840.2.da.b 840.da 105.p $48$ $6.707$ None \(0\) \(3\) \(3\) \(0\) $\mathrm{SU}(2)[C_{6}]$

Decomposition of \(S_{2}^{\mathrm{old}}(840, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(840, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(105, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(210, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(420, [\chi])\)\(^{\oplus 2}\)