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Properties

Label 840.2.cc
Level $840$
Weight $2$
Character orbit 840.cc
Rep. character $\chi_{840}(289,\cdot)$
Character field $\Q(\zeta_{6})$
Dimension $48$
Newform subspaces $3$
Sturm bound $384$
Trace bound $1$

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Defining parameters

Level: \( N \) \(=\) \( 840 = 2^{3} \cdot 3 \cdot 5 \cdot 7 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 840.cc (of order \(6\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 35 \)
Character field: \(\Q(\zeta_{6})\)
Newform subspaces: \( 3 \)
Sturm bound: \(384\)
Trace bound: \(1\)
Distinguishing \(T_p\): \(11\)

Dimensions

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

Total New Old
Modular forms 416 48 368
Cusp forms 352 48 304
Eisenstein series 64 0 64

Trace form

\( 48 q + 24 q^{9} + O(q^{10}) \) \( 48 q + 24 q^{9} + 4 q^{11} - 4 q^{15} + 20 q^{19} + 2 q^{25} - 4 q^{31} + 32 q^{35} + 24 q^{41} + 36 q^{49} - 12 q^{55} + 24 q^{59} + 24 q^{61} + 28 q^{65} + 32 q^{69} + 16 q^{71} + 8 q^{75} + 36 q^{79} - 24 q^{81} + 40 q^{85} - 24 q^{89} - 40 q^{91} + 8 q^{95} + 8 q^{99} + O(q^{100}) \)

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.cc.a 840.cc 35.j $4$ $6.707$ \(\Q(\zeta_{12})\) None \(0\) \(0\) \(-4\) \(0\) $\mathrm{SU}(2)[C_{6}]$ \(q+\zeta_{12}q^{3}+(-\zeta_{12}-2\zeta_{12}^{2}+\zeta_{12}^{3})q^{5}+\cdots\)
840.2.cc.b 840.cc 35.j $20$ $6.707$ \(\mathbb{Q}[x]/(x^{20} - \cdots)\) None \(0\) \(0\) \(2\) \(0\) $\mathrm{SU}(2)[C_{6}]$ \(q+(\beta _{6}+\beta _{15})q^{3}+(\beta _{1}+\beta _{11})q^{5}+(\beta _{1}+\cdots)q^{7}+\cdots\)
840.2.cc.c 840.cc 35.j $24$ $6.707$ None \(0\) \(0\) \(2\) \(0\) $\mathrm{SU}(2)[C_{6}]$

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

\( S_{2}^{\mathrm{old}}(840, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(35, [\chi])\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(70, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(105, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(140, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(210, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(280, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(420, [\chi])\)\(^{\oplus 2}\)