Space of modular forms of level 63, weight 12, and Character 63.e

• Label: 63.12.e
• Level: $63$
• Weight: $12$
• Character orbit: 63.e
• Rep. character: $\chi_{63}(37,\cdot)$
• Character field: $\Q(\zeta_{3})$
• Dimension: $72$
• Newform subspaces: $5$
• Sturm bound: $96$
• Trace bound: $1$

Defining parameters

Level:	\( N \)	\(=\)	\( 63 = 3^{2} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 12 \)
Character orbit:	\([\chi]\)	\(=\)	63.e (of order \(3\) and degree \(2\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 7 \)
Character field:			\(\Q(\zeta_{3})\)
Newform subspaces:			\( 5 \)
Sturm bound:			\(96\)
Trace bound:			\(1\)
Distinguishing \(T_p\):			\(2\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{12}(63, [\chi])\).

	Total	New	Old
Modular forms	184	76	108
Cusp forms	168	72	96
Eisenstein series	16	4	12

Trace form

72 * q + 24 * q^2 - 35324 * q^4 + 3720 * q^5 - 71918 * q^7 + 88824 * q^8 - 51910 * q^10 - 687414 * q^11 + 224660 * q^13 + 2644116 * q^14 - 36902132 * q^16 + 9942498 * q^17 - 19279198 * q^19 - 111232176 * q^20 + 69784124 * q^22 + 31117728 * q^23 - 262251014 * q^25 + 77363742 * q^26 + 353685504 * q^28 + 357657360 * q^29 - 282040370 * q^31 - 86006952 * q^32 - 25418004 * q^34 - 1016527794 * q^35 + 236448628 * q^37 + 344079228 * q^38 + 833901708 * q^40 - 18235932 * q^41 - 368613420 * q^43 - 830822916 * q^44 + 972788046 * q^46 + 2443636266 * q^47 - 3595173522 * q^49 - 16918407876 * q^50 + 5687198940 * q^52 + 3797492778 * q^53 + 987853528 * q^55 + 32564896752 * q^56 + 14860913816 * q^58 - 5016003360 * q^59 + 16227273242 * q^61 + 28186229136 * q^62 + 112006182696 * q^64 - 12662135058 * q^65 - 2375400082 * q^67 + 15034143600 * q^68 + 35044330090 * q^70 - 7234976628 * q^71 - 22026138764 * q^73 - 49323543612 * q^74 + 94630012992 * q^76 + 24023029146 * q^77 + 828151494 * q^79 + 185727435636 * q^80 - 76658724944 * q^82 - 196605396300 * q^83 + 73358484180 * q^85 + 16952051946 * q^86 + 81863023188 * q^88 + 307415215602 * q^89 - 235666106502 * q^91 - 871091121552 * q^92 - 277971492270 * q^94 - 138595501290 * q^95 + 352016029528 * q^97 + 903650350254 * q^98

Decomposition of \(S_{12}^{\mathrm{new}}(63, [\chi])\) 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
																		$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
63.12.e.a	$63$	$12$	63.e	7.c	$3$	$2$	$1$	$48.406$	\(\Q(\sqrt{-3}) \)	\(\Q(\sqrt{-3}) \)		✓			63.12.e.a	$4$	$0$	\(0\)	\(0\)	\(0\)	\(77153\)	$1$	$\mathrm{U}(1)[D_{3}]$	\(q+2^{11}\zeta_{6}q^{4}+(25807+25539\zeta_{6})q^{7}+\cdots\)
63.12.e.b	$63$	$12$	63.e	7.c	$3$	$12$	$6$	$48.406$	\(\mathbb{Q}[x]/(x^{12} - \cdots)\)	None					7.12.c.a	$2$	$0$	\(-22\)	\(0\)	\(8782\)	\(-504\)	$2^{20}\cdot 3^{5}\cdot 7^{6}$	$\mathrm{SU}(2)[C_{3}]$	\(q+(-4+\beta _{1}-4\beta _{2})q^{2}+(\beta _{1}+426\beta _{2}+\cdots)q^{4}+\cdots\)
63.12.e.c	$63$	$12$	63.e	7.c	$3$	$14$	$7$	$48.406$	\(\mathbb{Q}[x]/(x^{14} - \cdots)\)	None					21.12.e.a	$2$	$0$	\(-9\)	\(0\)	\(-7218\)	\(9219\)	$2^{12}\cdot 3^{7}\cdot 7^{8}$	$\mathrm{SU}(2)[C_{3}]$	\(q+(-1-\beta _{1}-\beta _{2})q^{2}+(1241\beta _{2}+11\beta _{3}+\cdots)q^{4}+\cdots\)
63.12.e.d	$63$	$12$	63.e	7.c	$3$	$16$	$8$	$48.406$	\(\mathbb{Q}[x]/(x^{16} - \cdots)\)	None					21.12.e.b	$2$	$0$	\(55\)	\(0\)	\(2156\)	\(-6560\)	$2^{10}\cdot 3^{9}\cdot 7^{10}$	$\mathrm{SU}(2)[C_{3}]$	\(q+(7+7\beta _{2}+\beta _{4})q^{2}+(7\beta _{1}+1346\beta _{2}+\cdots)q^{4}+\cdots\)
63.12.e.e	$63$	$12$	63.e	7.c	$3$	$28$	$14$	$48.406$		None		✓	✓		63.12.e.e	$4$	$0$	\(0\)	\(0\)	\(0\)	\(-151226\)		$\mathrm{SU}(2)[C_{3}]$

Decomposition of \(S_{12}^{\mathrm{old}}(63, [\chi])\) into lower level spaces

\( S_{12}^{\mathrm{old}}(63, [\chi]) \simeq \) \(S_{12}^{\mathrm{new}}(7, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{12}^{\mathrm{new}}(21, [\chi])\)\(^{\oplus 2}\)