Space of modular forms of level 25, weight 22, and Character 25.b

• Label: 25.22.b
• Level: $25$
• Weight: $22$
• Character orbit: 25.b
• Rep. character: $\chi_{25}(24,\cdot)$
• Character field: $\Q$
• Dimension: $30$
• Newform subspaces: $4$
• Sturm bound: $55$
• Trace bound: $1$

Defining parameters

Level:	\( N \)	\(=\)	\( 25 = 5^{2} \)
Weight:	\( k \)	\(=\)	\( 22 \)
Character orbit:	\([\chi]\)	\(=\)	25.b (of order \(2\) and degree \(1\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 5 \)
Character field:			\(\Q\)
Newform subspaces:			\( 4 \)
Sturm bound:			\(55\)
Trace bound:			\(1\)
Distinguishing \(T_p\):			\(2\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{22}(25, [\chi])\).

	Total	New	Old
Modular forms	56	32	24
Cusp forms	50	30	20
Eisenstein series	6	2	4

Trace form

30 * q - 31784210 * q^4 - 255239990 * q^6 - 63470082940 * q^9 - 149672541190 * q^11 - 1353236063220 * q^14 + 21447493499330 * q^16 + 123132251000750 * q^19 - 265422927060540 * q^21 + 1205399059072050 * q^24 + 2265353373536960 * q^26 - 164569712969200 * q^29 - 4896078559515940 * q^31 - 86326069811814770 * q^34 + 140633598903855380 * q^36 + 60003763528629520 * q^39 - 139065528110673890 * q^41 + 1103009961084390830 * q^44 - 415447702239256740 * q^46 - 1686128370327626110 * q^49 + 2396382025011502810 * q^51 - 162900238716610750 * q^54 - 7967681652412253700 * q^56 - 13315331503103310800 * q^59 - 21290087250584988140 * q^61 + 63374731145627475390 * q^64 - 155370579097575860230 * q^66 + 132596534411275324020 * q^69 - 140630609799154103840 * q^71 - 129335238840968771020 * q^74 - 694971214354978029150 * q^76 + 91683993735331179700 * q^79 - 973121420827319371370 * q^81 + 1114612598573483635980 * q^84 - 2278666698907408513240 * q^86 - 186508365879341918850 * q^89 - 2053013957212899420440 * q^91 + 3943532697562118094280 * q^94 - 9174408855691666335490 * q^96 + 1599274032036566714620 * q^99

Decomposition of \(S_{22}^{\mathrm{new}}(25, [\chi])\) 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
																		$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
25.22.b.a	$25$	$22$	25.b	5.b	$2$	$2$	$2$	$69.869$	\(\Q(\sqrt{-1}) \)	None					1.22.a.a	$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2$	$\mathrm{SU}(2)[C_{2}]$	\(q+144\beta q^{2}-64422\beta q^{3}+2014208 q^{4}+\cdots\)
25.22.b.b	$25$	$22$	25.b	5.b	$2$	$6$	$6$	$69.869$	\(\mathbb{Q}[x]/(x^{6} + \cdots)\)	None					5.22.a.a	$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2^{17}\cdot 3^{2}\cdot 5^{8}$	$\mathrm{SU}(2)[C_{2}]$	\(q+(-2\beta _{1}-\beta _{4})q^{2}+(-68\beta _{1}+7\beta _{4}+\cdots)q^{3}+\cdots\)
25.22.b.c	$25$	$22$	25.b	5.b	$2$	$8$	$8$	$69.869$	\(\mathbb{Q}[x]/(x^{8} + \cdots)\)	None					5.22.a.b	$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2^{16}\cdot 3^{2}\cdot 5^{14}\cdot 7^{2}$	$\mathrm{SU}(2)[C_{2}]$	\(q+(-\beta _{4}-\beta _{5})q^{2}+(-14\beta _{4}+11\beta _{5}+\cdots)q^{3}+\cdots\)
25.22.b.d	$25$	$22$	25.b	5.b	$2$	$14$	$14$	$69.869$	\(\mathbb{Q}[x]/(x^{14} + \cdots)\)	None		✓	✓		25.22.a.d	$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2^{26}\cdot 3^{6}\cdot 5^{50}\cdot 7^{4}$	$\mathrm{SU}(2)[C_{2}]$	\(q-\beta _{7}q^{2}+(-\beta _{7}+\beta _{9})q^{3}+(-1107130+\cdots)q^{4}+\cdots\)

Decomposition of \(S_{22}^{\mathrm{old}}(25, [\chi])\) into lower level spaces

\( S_{22}^{\mathrm{old}}(25, [\chi]) \simeq \) \(S_{22}^{\mathrm{new}}(5, [\chi])\)\(^{\oplus 2}\)