Properties

Label 336.4.h
Level $336$
Weight $4$
Character orbit 336.h
Rep. character $\chi_{336}(239,\cdot)$
Character field $\Q$
Dimension $36$
Newform subspaces $2$
Sturm bound $256$
Trace bound $1$

Related objects

Downloads

Learn more

Defining parameters

Level: \( N \) \(=\) \( 336 = 2^{4} \cdot 3 \cdot 7 \)
Weight: \( k \) \(=\) \( 4 \)
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: \(256\)
Trace bound: \(1\)
Distinguishing \(T_p\): \(5\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{4}(336, [\chi])\).

Total New Old
Modular forms 204 36 168
Cusp forms 180 36 144
Eisenstein series 24 0 24

Trace form

\( 36 q - 60 q^{9} + O(q^{10}) \) \( 36 q - 60 q^{9} - 900 q^{25} - 1152 q^{33} - 1584 q^{37} + 984 q^{45} - 1764 q^{49} - 3456 q^{57} - 1872 q^{61} + 744 q^{69} + 4968 q^{73} - 1836 q^{81} - 7272 q^{85} + 2472 q^{93} + 216 q^{97} + O(q^{100}) \)

Decomposition of \(S_{4}^{\mathrm{new}}(336, [\chi])\) into newform subspaces

Label Dim. \(A\) Field CM Traces $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
336.4.h.a $12$ $19.825$ \(\mathbb{Q}[x]/(x^{12} + \cdots)\) None \(0\) \(0\) \(0\) \(0\) \(q-\beta _{5}q^{3}+\beta _{8}q^{5}-\beta _{1}q^{7}+(6-\beta _{2}+\cdots)q^{9}+\cdots\)
336.4.h.b $24$ $19.825$ None \(0\) \(0\) \(0\) \(0\)

Decomposition of \(S_{4}^{\mathrm{old}}(336, [\chi])\) into lower level spaces

\( S_{4}^{\mathrm{old}}(336, [\chi]) \cong \) \(S_{4}^{\mathrm{new}}(12, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(48, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(84, [\chi])\)\(^{\oplus 3}\)