Space of modular forms of level 25, weight 18, and trivial character

• Label: 25.18.a
• Level: $25$
• Weight: $18$
• Character orbit: 25.a
• Rep. character: $\chi_{25}(1,\cdot)$
• Character field: $\Q$
• Dimension: $26$
• Newform subspaces: $6$
• Sturm bound: $45$
• Trace bound: $2$

Defining parameters

Level:	\( N \)	\(=\)	\( 25 = 5^{2} \)
Weight:	\( k \)	\(=\)	\( 18 \)
Character orbit:	\([\chi]\)	\(=\)	25.a (trivial)
Character field:			\(\Q\)
Newform subspaces:			\( 6 \)
Sturm bound:			\(45\)
Trace bound:			\(2\)
Distinguishing \(T_p\):			\(2\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{18}(\Gamma_0(25))\).

	Total	New	Old
Modular forms	45	29	16
Cusp forms	39	26	13
Eisenstein series	6	3	3

The following table gives the dimensions of the cuspidal new subspaces with specified eigenvalues for the Atkin-Lehner operators and the Fricke involution.

\(5\)		Total				Cusp				Eisenstein
		All	New	Old		All	New	Old		All	New	Old
\(+\)		\(22\)	\(13\)	\(9\)		\(19\)	\(12\)	\(7\)		\(3\)	\(1\)	\(2\)
\(-\)		\(23\)	\(16\)	\(7\)		\(20\)	\(14\)	\(6\)		\(3\)	\(2\)	\(1\)

Trace form

26 * q - 270 * q^2 - 680 * q^3 + 1676502 * q^4 + 12410442 * q^6 + 17455400 * q^7 - 59724360 * q^8 + 947330598 * q^9 + 171000072 * q^11 + 1480181360 * q^12 - 6318335660 * q^13 - 8454875556 * q^14 + 160847641426 * q^16 - 12452511660 * q^17 + 917672170 * q^18 + 85177880120 * q^19 - 489142862448 * q^21 + 345419135960 * q^22 + 228638179560 * q^23 + 556700120910 * q^24 + 1103384866092 * q^26 - 2162603332160 * q^27 + 2482395873440 * q^28 - 4772707616220 * q^29 + 67167501712 * q^31 + 4676455872480 * q^32 - 15448474623760 * q^33 + 24055959527734 * q^34 + 31521460698696 * q^36 - 19892387737980 * q^37 + 74749060253160 * q^38 + 82140177648336 * q^39 - 128530063011168 * q^41 - 375533825446560 * q^42 + 51970967913400 * q^43 + 379458801085794 * q^44 + 51233781869492 * q^46 - 511409671359240 * q^47 + 479672221530560 * q^48 + 1780207881219682 * q^49 + 512069181095472 * q^51 - 2198707771205400 * q^52 + 412566338722020 * q^53 + 3611380018434270 * q^54 - 1014420268602180 * q^56 - 6124255467297920 * q^57 + 2264134003590940 * q^58 + 3133490279381160 * q^59 - 1411998955028828 * q^61 - 10173175631927040 * q^62 + 8335669607765880 * q^63 + 27261402091684162 * q^64 - 3532900833287526 * q^66 - 8487446009539960 * q^67 + 2690660433588120 * q^68 + 5164324275942336 * q^69 + 20251526790577392 * q^71 - 23903772665479080 * q^72 - 2254738293282140 * q^73 + 12680228399558664 * q^74 + 16745997538342290 * q^76 - 8539648812070800 * q^77 + 16388995306689200 * q^78 + 33977812160424080 * q^79 - 25476157372193214 * q^81 + 40644729746359060 * q^82 - 36863782196340120 * q^83 - 171424852609075596 * q^84 - 158177334531563208 * q^86 + 104389795911892720 * q^87 - 38822651826925920 * q^88 + 26981736584732640 * q^89 - 57764305026598848 * q^91 + 200218516873878240 * q^92 - 30188693065948560 * q^93 - 553091859351383696 * q^94 + 599186469409058622 * q^96 + 293087044274217060 * q^97 - 213679878079784190 * q^98 - 509563323870568344 * q^99

Decomposition of \(S_{18}^{\mathrm{new}}(\Gamma_0(25))\) 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					A-L signs	Fricke sign	Coefficient ring index	Sato-Tate	$q$-expansion
																		$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$		5
25.18.a.a	$25$	$18$	25.a	1.a	$1$	$1$	$1$	$45.806$	\(\Q\)	None	✓				1.18.a.a	$1$	$1$	\(528\)	\(4284\)	\(0\)	\(-3225992\)		$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q+528q^{2}+4284q^{3}+147712q^{4}+\cdots\)
25.18.a.b	$25$	$18$	25.a	1.a	$1$	$2$	$2$	$45.806$	\(\Q(\sqrt{39}) \)	None	✓				5.18.a.a	$1$	$1$	\(-680\)	\(10980\)	\(0\)	\(22820700\)		$+$	$+$	$2^{2}\cdot 3^{2}$	$\mathrm{SU}(2)$	\(q+(-340+\beta )q^{2}+(5490-52\beta )q^{3}+\cdots\)
25.18.a.c	$25$	$18$	25.a	1.a	$1$	$3$	$3$	$45.806$	\(\mathbb{Q}[x]/(x^{3} - \cdots)\)	None	✓				5.18.a.b	$1$	$1$	\(-118\)	\(-15944\)	\(0\)	\(-2139308\)		$+$	$+$	$2^{3}\cdot 5$	$\mathrm{SU}(2)$	\(q+(-39+\beta _{1})q^{2}+(-5317-8\beta _{1}+\cdots)q^{3}+\cdots\)
25.18.a.d	$25$	$18$	25.a	1.a	$1$	$6$	$6$	$45.806$	\(\mathbb{Q}[x]/(x^{6} - \cdots)\)	None	✓	✓			25.18.a.d	$1$	$0$	\(-15\)	\(10640\)	\(0\)	\(17486200\)		$-$	$-$	$2^{11}\cdot 3^{3}\cdot 5^{7}$	$\mathrm{SU}(2)$	\(q+(-3+\beta _{1})q^{2}+(1769+9\beta _{1}+\beta _{2}+\cdots)q^{3}+\cdots\)
25.18.a.e	$25$	$18$	25.a	1.a	$1$	$6$	$6$	$45.806$	\(\mathbb{Q}[x]/(x^{6} - \cdots)\)	None	✓	✓	✓		25.18.a.d	$1$	$1$	\(15\)	\(-10640\)	\(0\)	\(-17486200\)		$+$	$+$	$2^{11}\cdot 3^{3}\cdot 5^{7}$	$\mathrm{SU}(2)$	\(q+(3-\beta _{1})q^{2}+(-1769-9\beta _{1}-\beta _{2}+\cdots)q^{3}+\cdots\)
25.18.a.f	$25$	$18$	25.a	1.a	$1$	$8$	$8$	$45.806$	\(\mathbb{Q}[x]/(x^{8} - \cdots)\)	None	✓		✓		5.18.b.a	$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)		$-$	$-$	$2^{21}\cdot 3^{8}\cdot 5^{14}\cdot 11$	$\mathrm{SU}(2)$	\(q+\beta _{1}q^{2}-\beta _{2}q^{3}+(72387+\beta _{4})q^{4}+\cdots\)

Decomposition of \(S_{18}^{\mathrm{old}}(\Gamma_0(25))\) into lower level spaces

\( S_{18}^{\mathrm{old}}(\Gamma_0(25)) \simeq \) \(S_{18}^{\mathrm{new}}(\Gamma_0(1))\)\(^{\oplus 3}\)\(\oplus\)\(S_{18}^{\mathrm{new}}(\Gamma_0(5))\)\(^{\oplus 2}\)