↑

Properties

Label 336.2.k
Level $336$
Weight $2$
Character orbit 336.k
Rep. character $\chi_{336}(209,\cdot)$
Character field $\Q$
Dimension $14$
Newform subspaces $3$
Sturm bound $128$
Trace bound $1$

Related objects

Downloads

Learn more

Defining parameters

Level: \( N \) \(=\) \( 336 = 2^{4} \cdot 3 \cdot 7 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 336.k (of order \(2\) and degree \(1\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 21 \)
Character field: \(\Q\)
Newform subspaces: \( 3 \)
Sturm bound: \(128\)
Trace bound: \(1\)
Distinguishing \(T_p\): \(5\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(336, [\chi])\).

Total New Old
Modular forms 76 18 58
Cusp forms 52 14 38
Eisenstein series 24 4 20

Trace form

\( 14 q + 4 q^{7} - 2 q^{9} + O(q^{10}) \) \( 14 q + 4 q^{7} - 2 q^{9} + 8 q^{15} - 2 q^{21} - 6 q^{25} - 4 q^{37} - 16 q^{39} + 32 q^{43} - 2 q^{49} - 4 q^{57} - 20 q^{63} - 16 q^{67} - 8 q^{79} - 18 q^{81} - 16 q^{85} - 24 q^{91} + 20 q^{93} - 64 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{2}^{\mathrm{new}}(336, [\chi])\) into newform subspaces

Label Char Prim Dim $A$ Field CM Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
336.2.k.a 336.k 21.c $2$ $2.683$ \(\Q(\sqrt{-3}) \) \(\Q(\sqrt{-3}) \) \(0\) \(0\) \(0\) \(-4\) $\mathrm{U}(1)[D_{2}]$ \(q-\zeta_{6}q^{3}+(-2-\zeta_{6})q^{7}-3q^{9}-4\zeta_{6}q^{13}+\cdots\)
336.2.k.b 336.k 21.c $4$ $2.683$ \(\Q(i, \sqrt{6})\) None \(0\) \(0\) \(0\) \(4\) $\mathrm{SU}(2)[C_{2}]$ \(q+\beta _{1}q^{3}+(\beta _{1}-\beta _{3})q^{5}+(1-\beta _{1}-\beta _{3})q^{7}+\cdots\)
336.2.k.c 336.k 21.c $8$ $2.683$ 8.0.342102016.5 None \(0\) \(0\) \(0\) \(4\) $\mathrm{SU}(2)[C_{2}]$ \(q+\beta _{1}q^{3}+\beta _{2}q^{5}+(1+\beta _{5})q^{7}+(-\beta _{5}+\cdots)q^{9}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(336, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(336, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(21, [\chi])\)\(^{\oplus 5}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(42, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(84, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(168, [\chi])\)\(^{\oplus 2}\)