Properties

Label 336.2.h
Level $336$
Weight $2$
Character orbit 336.h
Rep. character $\chi_{336}(239,\cdot)$
Character field $\Q$
Dimension $12$
Newform subspaces $2$
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.h (of order \(2\) and degree \(1\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 12 \)
Character field: \(\Q\)
Newform subspaces: \( 2 \)
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 12 64
Cusp forms 52 12 40
Eisenstein series 24 0 24

Trace form

\( 12 q + 12 q^{9} + O(q^{10}) \) \( 12 q + 12 q^{9} - 12 q^{25} + 48 q^{37} - 24 q^{45} - 12 q^{49} - 48 q^{61} + 24 q^{69} - 72 q^{73} - 36 q^{81} - 24 q^{85} + 24 q^{93} + 72 q^{97} + O(q^{100}) \)

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.h.a 336.h 12.b $4$ $2.683$ \(\Q(\zeta_{8})\) None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+(\zeta_{8}-\zeta_{8}^{3})q^{3}-\zeta_{8}^{2}q^{5}-\zeta_{8}q^{7}+\cdots\)
336.2.h.b 336.h 12.b $8$ $2.683$ 8.0.56070144.2 None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+\beta _{6}q^{3}+(\beta _{3}+\beta _{5})q^{5}+\beta _{4}q^{7}+(2+\cdots)q^{9}+\cdots\)

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

\( S_{2}^{\mathrm{old}}(336, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(48, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(84, [\chi])\)\(^{\oplus 3}\)