Space of modular forms of level 25, weight 9, and Character 25.c

• Label: 25.9.c
• Level: $25$
• Weight: $9$
• Character orbit: 25.c
• Rep. character: $\chi_{25}(7,\cdot)$
• Character field: $\Q(\zeta_{4})$
• Dimension: $22$
• Newform subspaces: $3$
• Sturm bound: $22$
• Trace bound: $1$

Defining parameters

Level:	\( N \)	\(=\)	\( 25 = 5^{2} \)
Weight:	\( k \)	\(=\)	\( 9 \)
Character orbit:	\([\chi]\)	\(=\)	25.c (of order \(4\) and degree \(2\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 5 \)
Character field:			\(\Q(i)\)
Newform subspaces:			\( 3 \)
Sturm bound:			\(22\)
Trace bound:			\(1\)
Distinguishing \(T_p\):			\(2\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{9}(25, [\chi])\).

	Total	New	Old
Modular forms	46	26	20
Cusp forms	34	22	12
Eisenstein series	12	4	8

Trace form

22 * q + 2 * q^2 + 72 * q^3 - 3516 * q^6 + 2352 * q^7 + 8220 * q^8 - 46396 * q^11 + 45912 * q^12 + 119142 * q^13 - 699388 * q^16 + 265502 * q^17 + 454062 * q^18 - 873216 * q^21 + 35664 * q^22 - 28888 * q^23 + 4344524 * q^26 - 392040 * q^27 - 1305192 * q^28 - 1695176 * q^31 - 3033928 * q^32 - 4269096 * q^33 + 9851772 * q^36 + 454002 * q^37 - 1443720 * q^38 + 8145284 * q^41 - 4223856 * q^42 - 792648 * q^43 - 33395736 * q^46 + 15313352 * q^47 + 21677712 * q^48 - 19367916 * q^51 + 735732 * q^52 + 13509122 * q^53 - 23241360 * q^56 + 34625520 * q^57 + 23903520 * q^58 - 57062296 * q^61 - 53913416 * q^62 - 44837688 * q^63 + 223372788 * q^66 + 32827752 * q^67 - 8118692 * q^68 - 154125736 * q^71 - 82596420 * q^72 - 111859638 * q^73 + 358863380 * q^76 - 26260136 * q^77 - 31125576 * q^78 - 81460278 * q^81 - 38023056 * q^82 + 14768432 * q^83 + 23310944 * q^86 + 133207680 * q^87 + 44555040 * q^88 + 50148624 * q^91 - 69931048 * q^92 + 96798024 * q^93 - 1381059876 * q^96 + 186656202 * q^97 + 345959698 * q^98

Decomposition of \(S_{9}^{\mathrm{new}}(25, [\chi])\) 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
																		$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
25.9.c.a	$25$	$9$	25.c	5.c	$4$	$4$	$2$	$10.184$	\(\Q(i, \sqrt{141})\)	None		✓			25.9.c.a	$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2^{3}$	$\mathrm{SU}(2)[C_{4}]$	\(q-\beta _{3}q^{2}+\beta _{2}q^{3}-26\beta _{1}q^{4}+282q^{6}+\cdots\)
25.9.c.b	$25$	$9$	25.c	5.c	$4$	$6$	$3$	$10.184$	\(\mathbb{Q}[x]/(x^{6} - \cdots)\)	None					5.9.c.a	$2$	$0$	\(2\)	\(72\)	\(0\)	\(2352\)	$2^{6}\cdot 5^{2}$	$\mathrm{SU}(2)[C_{4}]$	\(q+\beta _{3}q^{2}+(12+12\beta _{1}+\beta _{2}+\beta _{5})q^{3}+\cdots\)
25.9.c.c	$25$	$9$	25.c	5.c	$4$	$12$	$6$	$10.184$	\(\mathbb{Q}[x]/(x^{12} - \cdots)\)	None		✓	✓		25.9.c.c	$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2^{10}\cdot 3^{6}\cdot 5^{12}$	$\mathrm{SU}(2)[C_{4}]$	\(q-\beta _{2}q^{2}+(-\beta _{5}-\beta _{6}-\beta _{7})q^{3}+(281\beta _{1}+\cdots)q^{4}+\cdots\)

Decomposition of \(S_{9}^{\mathrm{old}}(25, [\chi])\) into lower level spaces

\( S_{9}^{\mathrm{old}}(25, [\chi]) \simeq \) \(S_{9}^{\mathrm{new}}(5, [\chi])\)\(^{\oplus 2}\)