Space of modular forms of level 21, weight 33, and Character 21.h

• Label: 21.33.h
• Level: $21$
• Weight: $33$
• Character orbit: 21.h
• Rep. character: $\chi_{21}(2,\cdot)$
• Character field: $\Q(\zeta_{6})$
• Dimension: $166$
• Newform subspaces: $2$
• Sturm bound: $88$
• Trace bound: $1$

Defining parameters

Level:	\( N \)	\(=\)	\( 21 = 3 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 33 \)
Character orbit:	\([\chi]\)	\(=\)	21.h (of order \(6\) and degree \(2\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 21 \)
Character field:			\(\Q(\zeta_{6})\)
Newform subspaces:			\( 2 \)
Sturm bound:			\(88\)
Trace bound:			\(1\)
Distinguishing \(T_p\):			\(2\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{33}(21, [\chi])\).

	Total	New	Old
Modular forms	174	174	0
Cusp forms	166	166	0
Eisenstein series	8	8	0

Trace form

\( 166 q - q^{3} + 171798691838 q^{4} + 3915256954876 q^{6} + 23283626657033 q^{7} - 620299214629855 q^{9} + O(q^{10}) \)

Decomposition of \(S_{33}^{\mathrm{new}}(21, [\chi])\) into newform subspaces

Label	Level	Weight	Char	Prim	Char order	Dim	Rel. Dim	$A$	Field	CM	Self-dual	Inner twists	Rank*	Traces				Coefficient ring index	Sato-Tate	$q$-expansion
														$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
21.33.h.a	$21$	$33$	21.h	21.h	$6$	$2$	$1$	$136.220$	\(\Q(\sqrt{-3}) \)	\(\Q(\sqrt{-3}) \)		$4$	$0$	\(0\)	\(-43046721\)	\(0\)	\(65\!\cdots\!59\)	$1$	$\mathrm{U}(1)[D_{6}]$	\(q-3^{16}\zeta_{6}q^{3}-2^{32}\zeta_{6}q^{4}+(36372171914815+\cdots)q^{7}+\cdots\)
21.33.h.b	$21$	$33$	21.h	21.h	$6$	$164$	$82$	$136.220$		None		$4$	$0$	\(0\)	\(43046720\)	\(0\)	\(-41\!\cdots\!26\)		$\mathrm{SU}(2)[C_{6}]$