Space of modular forms of level 12, weight 51, and Character 12.c

• Label: 12.51.c
• Level: $12$
• Weight: $51$
• Character orbit: 12.c
• Rep. character: $\chi_{12}(5,\cdot)$
• Character field: $\Q$
• Dimension: $17$
• Newform subspaces: $2$
• Sturm bound: $102$
• Trace bound: $1$

Defining parameters

Level:	\( N \)	\(=\)	\( 12 = 2^{2} \cdot 3 \)
Weight:	\( k \)	\(=\)	\( 51 \)
Character orbit:	\([\chi]\)	\(=\)	12.c (of order \(2\) and degree \(1\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 3 \)
Character field:			\(\Q\)
Newform subspaces:			\( 2 \)
Sturm bound:			\(102\)
Trace bound:			\(1\)
Distinguishing \(T_p\):			\(5\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{51}(12, [\chi])\).

	Total	New	Old
Modular forms	103	17	86
Cusp forms	97	17	80
Eisenstein series	6	0	6

Trace form

17 * q - 88437661203 * q^3 + 1346835075664713827362 * q^7 - 1146139217784456598082727 * q^9 + 7531162923337882394599910218 * q^13 - 91755057863258810998685925120 * q^15 - 19010962381103270316700559904518 * q^19 - 11426879334521446824460416185382 * q^21 - 413137209816718990557327225077987095 * q^25 + 1265903921694044758964309067883149333 * q^27 + 38180226204043801819855852602294805618 * q^31 - 107764008265732780083186770811598805760 * q^33 - 1289206419234223119201155360573528077574 * q^37 + 5898863342088107216420848512205815756642 * q^39 + 120137748253649168343710363733229971463498 * q^43 - 265780988784641735096911939370032246126080 * q^45 + 442707589860978960188293224102886350367875 * q^49 + 1336516162088228868225552286664441856199680 * q^51 + 28387755703369359493425866079582924077637120 * q^55 - 65422673972600911225841903009657718154946478 * q^57 + 161292348602636853614796911118462465686778538 * q^61 + 2254374423668477357845299946802950394017548978 * q^63 + 9979926734994804086559155103836890882269755482 * q^67 - 1630727771491685832699901726523292437595548160 * q^69 + 80334806158789146948360018651341588426174725234 * q^73 + 102646864702937555917930587235239375744832950885 * q^75 + 489013646077082116660296803613530143610869312786 * q^79 - 788012484697633575197526369297094144465465402143 * q^81 - 691416053482495482507590430421445047703251630080 * q^85 + 3122454747889097662093742105899335631840614900480 * q^87 - 11443180700839904656096679985629048991502439031148 * q^91 - 57755841123764623736102797262512096407228203989782 * q^93 + 15966610504570920643498358529324376785356847587362 * q^97 + 63435410054018146732994264871790240111196315742720 * q^99

Decomposition of \(S_{51}^{\mathrm{new}}(12, [\chi])\) into newform subspaces

Label	Level	Weight	Char	Prim	Char order	Dim	Rel. Dim	$A$	Field	CM	Self-dual	Twist minimal	Largest	Maximal	Minimal twist	Inner twists	Rank*	Traces				Coefficient ring index	Sato-Tate	$q$-expansion
																		$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
12.51.c.a	$12$	$51$	12.c	3.b	$2$	$1$	$1$	$190.003$	\(\Q\)	\(\Q(\sqrt{-3}) \)	✓	✓			12.51.c.a	$2$	$0$	\(0\)	\(-847288609443\)	\(0\)	\(-11\!\cdots\!18\)	$1$	$\mathrm{U}(1)[D_{2}]$	\(q-3^{25}q^{3}-1147513263675748744318q^{7}+\cdots\)
12.51.c.b	$12$	$51$	12.c	3.b	$2$	$16$	$16$	$190.003$	\(\mathbb{Q}[x]/(x^{16} + \cdots)\)	None		✓	✓		12.51.c.b	$2$	$0$	\(0\)	\(758850948240\)	\(0\)	\(24\!\cdots\!80\)	$2^{247}\cdot 3^{179}\cdot 5^{20}\cdot 7^{9}\cdot 17^{2}$	$\mathrm{SU}(2)[C_{2}]$	\(q+(47428184265+\beta _{1})q^{3}+(8013\beta _{1}+\cdots)q^{5}+\cdots\)

Decomposition of \(S_{51}^{\mathrm{old}}(12, [\chi])\) into lower level spaces

\( S_{51}^{\mathrm{old}}(12, [\chi]) \simeq \) \(S_{51}^{\mathrm{new}}(3, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{51}^{\mathrm{new}}(6, [\chi])\)\(^{\oplus 2}\)