Properties

Label 336.7.bh
Level $336$
Weight $7$
Character orbit 336.bh
Rep. character $\chi_{336}(145,\cdot)$
Character field $\Q(\zeta_{6})$
Dimension $96$
Newform subspaces $8$
Sturm bound $448$
Trace bound $5$

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Defining parameters

Level: \( N \) \(=\) \( 336 = 2^{4} \cdot 3 \cdot 7 \)
Weight: \( k \) \(=\) \( 7 \)
Character orbit: \([\chi]\) \(=\) 336.bh (of order \(6\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 7 \)
Character field: \(\Q(\zeta_{6})\)
Newform subspaces: \( 8 \)
Sturm bound: \(448\)
Trace bound: \(5\)
Distinguishing \(T_p\): \(5\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{7}(336, [\chi])\).

Total New Old
Modular forms 792 96 696
Cusp forms 744 96 648
Eisenstein series 48 0 48

Trace form

\( 96 q + 360 q^{7} + 11664 q^{9} + O(q^{10}) \) \( 96 q + 360 q^{7} + 11664 q^{9} - 1360 q^{11} - 15120 q^{19} - 24368 q^{23} + 161928 q^{25} + 66400 q^{29} + 27720 q^{31} + 13608 q^{33} - 147120 q^{35} + 3600 q^{37} + 68040 q^{39} + 101760 q^{43} - 376992 q^{47} + 182928 q^{49} - 100320 q^{53} - 136080 q^{57} - 1329216 q^{59} - 529200 q^{61} - 87480 q^{63} + 266000 q^{65} + 450336 q^{67} - 1285248 q^{71} + 385560 q^{73} + 241040 q^{77} - 696648 q^{79} - 2834352 q^{81} - 650592 q^{85} + 3591696 q^{91} - 664848 q^{93} - 2936544 q^{95} - 660960 q^{99} + O(q^{100}) \)

Decomposition of \(S_{7}^{\mathrm{new}}(336, [\chi])\) into newform subspaces

Label Dim. \(A\) Field CM Traces $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\)
336.7.bh.a \(8\) \(77.298\) \(\mathbb{Q}[x]/(x^{8} - \cdots)\) None \(0\) \(-108\) \(-294\) \(-232\) \(q+(-9-9\beta _{1})q^{3}+(-7^{2}+5^{2}\beta _{1}-\beta _{2}+\cdots)q^{5}+\cdots\)
336.7.bh.b \(8\) \(77.298\) \(\mathbb{Q}[x]/(x^{8} - \cdots)\) None \(0\) \(-108\) \(-42\) \(-748\) \(q+(-9+9\beta _{2})q^{3}+(-7-3\beta _{2}+\beta _{3}+\cdots)q^{5}+\cdots\)
336.7.bh.c \(8\) \(77.298\) \(\mathbb{Q}[x]/(x^{8} - \cdots)\) None \(0\) \(-108\) \(210\) \(608\) \(q+(-18+9\beta _{2})q^{3}+(15-5\beta _{1}+20\beta _{2}+\cdots)q^{5}+\cdots\)
336.7.bh.d \(8\) \(77.298\) \(\mathbb{Q}[x]/(x^{8} - \cdots)\) None \(0\) \(108\) \(-294\) \(656\) \(q+(18-9\beta _{1})q^{3}+(-24-5^{2}\beta _{1}+\beta _{2}+\cdots)q^{5}+\cdots\)
336.7.bh.e \(8\) \(77.298\) \(\mathbb{Q}[x]/(x^{8} - \cdots)\) None \(0\) \(108\) \(-42\) \(92\) \(q+(9-9\beta _{1})q^{3}+(-7-3\beta _{1}+\beta _{4})q^{5}+\cdots\)
336.7.bh.f \(8\) \(77.298\) \(\mathbb{Q}[x]/(x^{8} - \cdots)\) None \(0\) \(108\) \(462\) \(-580\) \(q+(9-9\beta _{1})q^{3}+(77+39\beta _{1}+\beta _{2}-\beta _{4}+\cdots)q^{5}+\cdots\)
336.7.bh.g \(24\) \(77.298\) None \(0\) \(-324\) \(126\) \(552\)
336.7.bh.h \(24\) \(77.298\) None \(0\) \(324\) \(-126\) \(12\)

Decomposition of \(S_{7}^{\mathrm{old}}(336, [\chi])\) into lower level spaces

\( S_{7}^{\mathrm{old}}(336, [\chi]) \cong \) \(S_{7}^{\mathrm{new}}(7, [\chi])\)\(^{\oplus 10}\)\(\oplus\)\(S_{7}^{\mathrm{new}}(14, [\chi])\)\(^{\oplus 8}\)\(\oplus\)\(S_{7}^{\mathrm{new}}(21, [\chi])\)\(^{\oplus 5}\)\(\oplus\)\(S_{7}^{\mathrm{new}}(28, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{7}^{\mathrm{new}}(42, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{7}^{\mathrm{new}}(56, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{7}^{\mathrm{new}}(84, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{7}^{\mathrm{new}}(112, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{7}^{\mathrm{new}}(168, [\chi])\)\(^{\oplus 2}\)