Properties

Label 336.4.bc
Level $336$
Weight $4$
Character orbit 336.bc
Rep. character $\chi_{336}(17,\cdot)$
Character field $\Q(\zeta_{6})$
Dimension $92$
Newform subspaces $6$
Sturm bound $256$
Trace bound $3$

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Defining parameters

Level: \( N \) \(=\) \( 336 = 2^{4} \cdot 3 \cdot 7 \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 336.bc (of order \(6\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 21 \)
Character field: \(\Q(\zeta_{6})\)
Newform subspaces: \( 6 \)
Sturm bound: \(256\)
Trace bound: \(3\)
Distinguishing \(T_p\): \(5\), \(13\)

Dimensions

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

Total New Old
Modular forms 408 100 308
Cusp forms 360 92 268
Eisenstein series 48 8 40

Trace form

\( 92q + 3q^{3} - 14q^{7} - q^{9} + O(q^{10}) \) \( 92q + 3q^{3} - 14q^{7} - q^{9} - 50q^{15} + 276q^{19} - 97q^{21} - 868q^{25} - 624q^{31} - 3q^{33} - 2q^{37} - 302q^{39} - 580q^{43} - 663q^{45} - 388q^{49} + 141q^{51} + 790q^{57} - 6q^{61} - 1207q^{63} - 1192q^{67} - 330q^{73} + 222q^{75} + 1124q^{79} + 459q^{81} - 804q^{85} + 3756q^{87} - 3822q^{91} + q^{93} - 3566q^{99} + O(q^{100}) \)

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.bc.a \(2\) \(19.825\) \(\Q(\sqrt{-3}) \) \(\Q(\sqrt{-3}) \) \(0\) \(-9\) \(0\) \(-37\) \(q+(-3-3\zeta_{6})q^{3}+(-18-\zeta_{6})q^{7}+\cdots\)
336.4.bc.b \(2\) \(19.825\) \(\Q(\sqrt{-3}) \) \(\Q(\sqrt{-3}) \) \(0\) \(9\) \(0\) \(17\) \(q+(3+3\zeta_{6})q^{3}+(18-19\zeta_{6})q^{7}+3^{3}\zeta_{6}q^{9}+\cdots\)
336.4.bc.c \(12\) \(19.825\) \(\mathbb{Q}[x]/(x^{12} - \cdots)\) None \(0\) \(0\) \(0\) \(42\) \(q+(-\beta _{3}+\beta _{4})q^{3}-\beta _{11}q^{5}+(2-2\beta _{1}+\cdots)q^{7}+\cdots\)
336.4.bc.d \(12\) \(19.825\) \(\mathbb{Q}[x]/(x^{12} - \cdots)\) None \(0\) \(3\) \(0\) \(56\) \(q+\beta _{1}q^{3}+\beta _{4}q^{5}+(4+2\beta _{1}+3\beta _{2}+\cdots)q^{7}+\cdots\)
336.4.bc.e \(16\) \(19.825\) \(\mathbb{Q}[x]/(x^{16} - \cdots)\) None \(0\) \(0\) \(0\) \(-80\) \(q-\beta _{4}q^{3}-\beta _{9}q^{5}+(-6-\beta _{1}-2\beta _{2}+\cdots)q^{7}+\cdots\)
336.4.bc.f \(48\) \(19.825\) None \(0\) \(0\) \(0\) \(-12\)

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

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