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Properties

Label 336.3.m
Level $336$
Weight $3$
Character orbit 336.m
Rep. character $\chi_{336}(127,\cdot)$
Character field $\Q$
Dimension $12$
Newform subspaces $3$
Sturm bound $192$
Trace bound $5$

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Defining parameters

Level: \( N \) \(=\) \( 336 = 2^{4} \cdot 3 \cdot 7 \)
Weight: \( k \) \(=\) \( 3 \)
Character orbit: \([\chi]\) \(=\) 336.m (of order \(2\) and degree \(1\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 4 \)
Character field: \(\Q\)
Newform subspaces: \( 3 \)
Sturm bound: \(192\)
Trace bound: \(5\)
Distinguishing \(T_p\): \(5\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{3}(336, [\chi])\).

Total New Old
Modular forms 140 12 128
Cusp forms 116 12 104
Eisenstein series 24 0 24

Trace form

\( 12 q - 24 q^{5} - 36 q^{9} + O(q^{10}) \) \( 12 q - 24 q^{5} - 36 q^{9} + 72 q^{13} + 24 q^{17} - 12 q^{25} - 120 q^{29} - 24 q^{37} + 120 q^{41} + 72 q^{45} - 84 q^{49} + 168 q^{53} - 120 q^{61} - 144 q^{65} - 72 q^{73} + 108 q^{81} - 96 q^{85} + 216 q^{89} + 144 q^{93} - 72 q^{97} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{3}^{\mathrm{new}}(336, [\chi])\) into newform subspaces

Label Char Prim Dim $A$ Field CM Minimal twist Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
336.3.m.a 336.m 4.b $4$ $9.155$ \(\Q(\sqrt{-3}, \sqrt{-7})\) None 336.3.m.a \(0\) \(0\) \(-20\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q-\beta _{2}q^{3}+(-5+\beta _{1})q^{5}+\beta _{3}q^{7}-3q^{9}+\cdots\)
336.3.m.b 336.m 4.b $4$ $9.155$ \(\Q(\sqrt{-3}, \sqrt{-7})\) None 336.3.m.b \(0\) \(0\) \(-8\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q-\beta _{2}q^{3}-2q^{5}-\beta _{3}q^{7}-3q^{9}+(4\beta _{2}+\cdots)q^{11}+\cdots\)
336.3.m.c 336.m 4.b $4$ $9.155$ \(\Q(\sqrt{-3}, \sqrt{-7})\) None 336.3.m.c \(0\) \(0\) \(4\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+\beta _{2}q^{3}+(1-\beta _{1})q^{5}-\beta _{3}q^{7}-3q^{9}+\cdots\)

Decomposition of \(S_{3}^{\mathrm{old}}(336, [\chi])\) into lower level spaces

\( S_{3}^{\mathrm{old}}(336, [\chi]) \simeq \) \(S_{3}^{\mathrm{new}}(12, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(16, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(28, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(48, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(84, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(112, [\chi])\)\(^{\oplus 2}\)