Space of modular forms of level 25, weight 26, and Character 25.b

• Label: 25.26.b
• Level: $25$
• Weight: $26$
• Character orbit: 25.b
• Rep. character: $\chi_{25}(24,\cdot)$
• Character field: $\Q$
• Dimension: $36$
• Newform subspaces: $4$
• Sturm bound: $65$
• Trace bound: $1$

Defining parameters

Level:	\( N \)	\(=\)	\( 25 = 5^{2} \)
Weight:	\( k \)	\(=\)	\( 26 \)
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:			\(65\)
Trace bound:			\(1\)
Distinguishing \(T_p\):			\(2\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{26}(25, [\chi])\).

	Total	New	Old
Modular forms	66	38	28
Cusp forms	60	36	24
Eisenstein series	6	2	4

Trace form

36 * q - 639695442 * q^4 - 16762414838 * q^6 - 8813449216228 * q^9 + 7109701558272 * q^11 + 1166301548592876 * q^14 + 9662784091065666 * q^16 - 33210594985316160 * q^19 + 23493002696648352 * q^21 + 1851570523728579570 * q^24 - 137167925806876608 * q^26 + 3010316105426220360 * q^29 + 4206304574072880672 * q^31 + 83135752624207687566 * q^34 + 89476277144906251316 * q^36 - 20603479169570796416 * q^39 + 299390759758918911672 * q^41 - 3323154579693629762034 * q^44 + 1277853424977966957372 * q^46 - 7208718621685548690852 * q^49 - 445206593785461348368 * q^51 + 22358538375378667221890 * q^54 - 27364578953112399314340 * q^56 + 3992076194391648627120 * q^59 - 18951337192635821105928 * q^61 - 242758840163918913546882 * q^64 - 143790336546696831399526 * q^66 - 643966000944406310950656 * q^69 + 323910889598230509123072 * q^71 + 317870504323094299682196 * q^74 - 1217952562128321209028030 * q^76 + 2934879397487392750887360 * q^79 + 2116173229480430027508676 * q^81 + 5011295157194626005253356 * q^84 - 16146194672702641888736568 * q^86 + 11228203550922517997925480 * q^89 - 11017852528385703258168768 * q^91 + 17628810725672327103824136 * q^94 - 58852270969590399193737538 * q^96 + 1390032522174891051644944 * q^99

Decomposition of \(S_{26}^{\mathrm{new}}(25, [\chi])\) 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
																		$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
25.26.b.a	$25$	$26$	25.b	5.b	$2$	$2$	$2$	$98.999$	\(\Q(\sqrt{-1}) \)	None					1.26.a.a	$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2$	$\mathrm{SU}(2)[C_{2}]$	\(q+24\beta q^{2}-97902\beta q^{3}+33552128 q^{4}+\cdots\)
25.26.b.b	$25$	$26$	25.b	5.b	$2$	$8$	$8$	$98.999$	\(\mathbb{Q}[x]/(x^{8} + \cdots)\)	None					5.26.a.a	$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2^{32}\cdot 3^{4}\cdot 5^{16}$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta _{4}q^{2}+(17\beta _{4}+158\beta _{5}+\beta _{6})q^{3}+\cdots\)
25.26.b.c	$25$	$26$	25.b	5.b	$2$	$10$	$10$	$98.999$	\(\mathbb{Q}[x]/(x^{10} + \cdots)\)	None					5.26.a.b	$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2^{29}\cdot 3^{6}\cdot 5^{24}$	$\mathrm{SU}(2)[C_{2}]$	\(q-\beta _{5}q^{2}+(5^{2}\beta _{5}-24\beta _{6}-\beta _{7})q^{3}+\cdots\)
25.26.b.d	$25$	$26$	25.b	5.b	$2$	$16$	$16$	$98.999$	\(\mathbb{Q}[x]/(x^{16} + \cdots)\)	None		✓	✓		25.26.a.d	$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2^{38}\cdot 3^{14}\cdot 5^{66}$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta _{1}q^{2}+(23\beta _{1}+\beta _{10})q^{3}+(-21241963+\cdots)q^{4}+\cdots\)

Decomposition of \(S_{26}^{\mathrm{old}}(25, [\chi])\) into lower level spaces

\( S_{26}^{\mathrm{old}}(25, [\chi]) \simeq \) \(S_{26}^{\mathrm{new}}(5, [\chi])\)\(^{\oplus 2}\)