Space of modular forms of level 252, weight 5, and Character 252.z

• Label: 252.5.z
• Level: $252$
• Weight: $5$
• Character orbit: 252.z
• Rep. character: $\chi_{252}(73,\cdot)$
• Character field: $\Q(\zeta_{6})$
• Dimension: $26$
• Newform subspaces: $6$
• Sturm bound: $240$
• Trace bound: $7$

Defining parameters

Level:	\( N \)	\(=\)	\( 252 = 2^{2} \cdot 3^{2} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 5 \)
Character orbit:	\([\chi]\)	\(=\)	252.z (of order \(6\) and degree \(2\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 7 \)
Character field:			\(\Q(\zeta_{6})\)
Newform subspaces:			\( 6 \)
Sturm bound:			\(240\)
Trace bound:			\(7\)
Distinguishing \(T_p\):			\(5\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{5}(252, [\chi])\).

	Total	New	Old
Modular forms	408	26	382
Cusp forms	360	26	334
Eisenstein series	48	0	48

Trace form

26 * q - 27 * q^5 + 16 * q^7 - 21 * q^11 + 243 * q^17 + 603 * q^19 + 57 * q^23 + 1172 * q^25 + 60 * q^29 + 1239 * q^31 - 1299 * q^35 - 151 * q^37 + 5720 * q^43 + 2781 * q^47 + 7028 * q^49 + 2565 * q^53 + 6867 * q^59 + 12837 * q^61 + 1398 * q^65 + 3793 * q^67 - 11544 * q^71 + 6255 * q^73 - 7683 * q^77 - 4679 * q^79 + 5778 * q^85 + 4059 * q^89 + 9870 * q^91 + 12273 * q^95

Decomposition of \(S_{5}^{\mathrm{new}}(252, [\chi])\) 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
																		$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
252.5.z.a	$252$	$5$	252.z	7.d	$6$	$2$	$1$	$26.049$	\(\Q(\sqrt{-3}) \)	\(\Q(\sqrt{-3}) \)		✓			252.5.z.a	$4$	$0$	\(0\)	\(0\)	\(0\)	\(-23\)	$1$	$\mathrm{U}(1)[D_{6}]$	\(q+(2^{4}-55\zeta_{6})q^{7}+(-15+30\zeta_{6})q^{13}+\cdots\)
252.5.z.b	$252$	$5$	252.z	7.d	$6$	$4$	$2$	$26.049$	\(\Q(\sqrt{-3}, \sqrt{-19})\)	None					84.5.m.a	$2$	$0$	\(0\)	\(0\)	\(-39\)	\(-70\)	$3^{2}$	$\mathrm{SU}(2)[C_{6}]$	\(q+(-13+3\beta _{1}-5\beta _{2})q^{5}+(-14-7\beta _{1}+\cdots)q^{7}+\cdots\)
252.5.z.c	$252$	$5$	252.z	7.d	$6$	$4$	$2$	$26.049$	\(\Q(\sqrt{-3}, \sqrt{14})\)	None		✓			252.5.z.c	$4$	$0$	\(0\)	\(0\)	\(0\)	\(-154\)	$2^{2}\cdot 3^{3}$	$\mathrm{SU}(2)[C_{6}]$	\(q+\beta _{3}q^{5}+(-56-35\beta _{1})q^{7}+(2\beta _{2}+\cdots)q^{11}+\cdots\)
252.5.z.d	$252$	$5$	252.z	7.d	$6$	$4$	$2$	$26.049$	\(\Q(\sqrt{-3}, \sqrt{133})\)	None		✓			252.5.z.d	$4$	$0$	\(0\)	\(0\)	\(0\)	\(182\)	$2^{2}\cdot 3$	$\mathrm{SU}(2)[C_{6}]$	\(q+\beta _{2}q^{5}+(56-21\beta _{1})q^{7}+(-5\beta _{2}+\cdots)q^{11}+\cdots\)
252.5.z.e	$252$	$5$	252.z	7.d	$6$	$6$	$3$	$26.049$	6.0.\(\cdots\).2	None					84.5.m.b	$2$	$0$	\(0\)	\(0\)	\(-15\)	\(15\)	$2^{2}\cdot 3^{2}\cdot 7$	$\mathrm{SU}(2)[C_{6}]$	\(q+(-1-2\beta _{1}-\beta _{3})q^{5}+(3+\beta _{2}-2\beta _{3}+\cdots)q^{7}+\cdots\)
252.5.z.f	$252$	$5$	252.z	7.d	$6$	$6$	$3$	$26.049$	6.0.11337408.1	None					28.5.h.a	$2$	$0$	\(0\)	\(0\)	\(27\)	\(66\)	$2^{2}\cdot 3^{3}\cdot 7^{2}$	$\mathrm{SU}(2)[C_{6}]$	\(q+(3+3\beta _{1}+\beta _{2}-\beta _{4})q^{5}+(9+4\beta _{1}+\cdots)q^{7}+\cdots\)

Decomposition of \(S_{5}^{\mathrm{old}}(252, [\chi])\) into lower level spaces

\( S_{5}^{\mathrm{old}}(252, [\chi]) \simeq \) \(S_{5}^{\mathrm{new}}(7, [\chi])\)\(^{\oplus 9}\)\(\oplus\)\(S_{5}^{\mathrm{new}}(14, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{5}^{\mathrm{new}}(21, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{5}^{\mathrm{new}}(28, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{5}^{\mathrm{new}}(42, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{5}^{\mathrm{new}}(63, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{5}^{\mathrm{new}}(84, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{5}^{\mathrm{new}}(126, [\chi])\)\(^{\oplus 2}\)