Space of modular forms of level 925, weight 2, and Character 925.bb

• Label: 925.2.bb
• Level: $925$
• Weight: $2$
• Character orbit: 925.bb
• Rep. character: $\chi_{925}(151,\cdot)$
• Character field: $\Q(\zeta_{18})$
• Dimension: $342$
• Newform subspaces: $5$
• Sturm bound: $190$
• Trace bound: $2$

Defining parameters

Level:	\( N \)	\(=\)	\( 925 = 5^{2} \cdot 37 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	925.bb (of order \(18\) and degree \(6\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 37 \)
Character field:			\(\Q(\zeta_{18})\)
Newform subspaces:			\( 5 \)
Sturm bound:			\(190\)
Trace bound:			\(2\)
Distinguishing \(T_p\):			\(2\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(925, [\chi])\).

	Total	New	Old
Modular forms	612	378	234
Cusp forms	540	342	198
Eisenstein series	72	36	36

Trace form

342 * q + 3 * q^2 + 9 * q^3 + 9 * q^4 + 9 * q^7 + 18 * q^8 + 3 * q^9 - 21 * q^11 - 33 * q^12 + 21 * q^13 - 9 * q^14 - 3 * q^16 + 15 * q^17 + 24 * q^18 + 6 * q^19 - 30 * q^21 - 15 * q^22 + 9 * q^23 - 51 * q^24 + 33 * q^26 + 3 * q^27 - 3 * q^28 + 36 * q^32 + 6 * q^33 - 15 * q^34 - 276 * q^36 + 42 * q^37 - 6 * q^38 - 12 * q^39 + 12 * q^41 - 105 * q^42 + 102 * q^44 + 18 * q^46 - 30 * q^47 + 21 * q^48 + 75 * q^49 + 63 * q^51 - 9 * q^52 + 15 * q^53 - 51 * q^54 - 81 * q^56 + 3 * q^57 - 87 * q^58 + 12 * q^59 - 138 * q^61 + 24 * q^62 - 21 * q^63 + 72 * q^64 + 261 * q^66 - 30 * q^67 + 114 * q^69 - 3 * q^71 + 33 * q^72 + 30 * q^73 + 3 * q^74 + 75 * q^76 - 75 * q^77 - 51 * q^78 + 30 * q^79 + 81 * q^81 + 45 * q^82 - 24 * q^83 + 54 * q^84 - 186 * q^86 - 105 * q^87 - 144 * q^88 + 81 * q^91 + 36 * q^92 - 84 * q^93 + 102 * q^94 - 15 * q^96 + 81 * q^97 + 99 * q^98 - 294 * q^99

Decomposition of \(S_{2}^{\mathrm{new}}(925, [\chi])\) 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
																		$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
925.2.bb.a	$925$	$2$	925.bb	37.h	$18$	$18$	$3$	$7.386$	\(\mathbb{Q}[x]/(x^{18} + \cdots)\)	None					37.2.h.a	$2$	$0$	\(9\)	\(9\)	\(0\)	\(3\)	$1$	$\mathrm{SU}(2)[C_{18}]$	\(q+(-\beta _{4}+\beta _{11})q^{2}+(1+\beta _{12}-\beta _{16}+\cdots)q^{3}+\cdots\)
925.2.bb.b	$925$	$2$	925.bb	37.h	$18$	$72$	$12$	$7.386$		None					185.2.w.a	$2$	$0$	\(-6\)	\(0\)	\(0\)	\(6\)		$\mathrm{SU}(2)[C_{18}]$
925.2.bb.c	$925$	$2$	925.bb	37.h	$18$	$78$	$13$	$7.386$		None		✓			925.2.bb.c	$2$	$0$	\(-3\)	\(0\)	\(0\)	\(6\)		$\mathrm{SU}(2)[C_{18}]$
925.2.bb.d	$925$	$2$	925.bb	37.h	$18$	$78$	$13$	$7.386$		None		✓			925.2.bb.c	$2$	$0$	\(3\)	\(0\)	\(0\)	\(-6\)		$\mathrm{SU}(2)[C_{18}]$
925.2.bb.e	$925$	$2$	925.bb	37.h	$18$	$96$	$16$	$7.386$		None			✓		185.2.v.a	$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)		$\mathrm{SU}(2)[C_{18}]$

Decomposition of \(S_{2}^{\mathrm{old}}(925, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(925, [\chi]) \simeq \) \(S_{2}^{\mathrm{new}}(37, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(185, [\chi])\)\(^{\oplus 2}\)