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Properties

Label 336.3.d
Level $336$
Weight $3$
Character orbit 336.d
Rep. character $\chi_{336}(113,\cdot)$
Character field $\Q$
Dimension $24$
Newform subspaces $4$
Sturm bound $192$
Trace bound $3$

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Defining parameters

Level: \( N \) \(=\) \( 336 = 2^{4} \cdot 3 \cdot 7 \)
Weight: \( k \) \(=\) \( 3 \)
Character orbit: \([\chi]\) \(=\) 336.d (of order \(2\) and degree \(1\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 3 \)
Character field: \(\Q\)
Newform subspaces: \( 4 \)
Sturm bound: \(192\)
Trace bound: \(3\)
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 24 116
Cusp forms 116 24 92
Eisenstein series 24 0 24

Trace form

\( 24 q + 8 q^{9} + O(q^{10}) \) \( 24 q + 8 q^{9} + 48 q^{15} + 32 q^{19} - 120 q^{25} - 144 q^{27} - 64 q^{31} - 48 q^{33} - 32 q^{37} + 144 q^{39} + 64 q^{43} + 168 q^{49} - 96 q^{51} - 224 q^{55} + 112 q^{57} + 192 q^{61} + 256 q^{67} - 48 q^{73} + 80 q^{75} - 136 q^{81} - 400 q^{85} + 32 q^{87} - 48 q^{93} + 240 q^{97} + 64 q^{99} + O(q^{100}) \)

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.d.a 336.d 3.b $4$ $9.155$ 4.0.116032.1 None 84.3.c.a \(0\) \(-6\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+(-2-\beta _{2})q^{3}+(2-\beta _{1}+\beta _{2}+2\beta _{3})q^{5}+\cdots\)
336.3.d.b 336.d 3.b $4$ $9.155$ \(\Q(\sqrt{-2}, \sqrt{7})\) None 42.3.b.a \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+(\beta _{1}-\beta _{3})q^{3}+(-2\beta _{1}+\beta _{2})q^{5}+\beta _{3}q^{7}+\cdots\)
336.3.d.c 336.d 3.b $4$ $9.155$ 4.0.65856.1 None 21.3.b.a \(0\) \(2\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+(1-\beta _{1}+\beta _{3})q^{3}+(1-\beta _{2}+2\beta _{3})q^{5}+\cdots\)
336.3.d.d 336.d 3.b $12$ $9.155$ \(\mathbb{Q}[x]/(x^{12} - \cdots)\) None 168.3.d.a \(0\) \(4\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q-\beta _{3}q^{3}+(\beta _{3}+\beta _{9})q^{5}+\beta _{1}q^{7}+(\beta _{2}+\cdots)q^{9}+\cdots\)

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

\( S_{3}^{\mathrm{old}}(336, [\chi]) \simeq \) \(S_{3}^{\mathrm{new}}(12, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(21, [\chi])\)\(^{\oplus 5}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(24, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(42, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(48, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(84, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(168, [\chi])\)\(^{\oplus 2}\)