Space of modular forms of level 1125, weight 2, and Character 1125.b

• Label: 1125.2.b
• Level: $1125$
• Weight: $2$
• Character orbit: 1125.b
• Rep. character: $\chi_{1125}(874,\cdot)$
• Character field: $\Q$
• Dimension: $40$
• Newform subspaces: $8$
• Sturm bound: $300$
• Trace bound: $11$

Defining parameters

Level:	\( N \)	\(=\)	\( 1125 = 3^{2} \cdot 5^{3} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1125.b (of order \(2\) and degree \(1\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 5 \)
Character field:			\(\Q\)
Newform subspaces:			\( 8 \)
Sturm bound:			\(300\)
Trace bound:			\(11\)
Distinguishing \(T_p\):			\(2\), \(7\), \(11\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(1125, [\chi])\).

	Total	New	Old
Modular forms	170	40	130
Cusp forms	130	40	90
Eisenstein series	40	0	40

Trace form

40 * q - 42 * q^4 + 4 * q^14 + 42 * q^16 + 14 * q^19 + 2 * q^26 - 6 * q^29 - 10 * q^31 + 2 * q^34 - 2 * q^41 - 54 * q^44 + 42 * q^46 - 14 * q^49 + 50 * q^56 + 58 * q^59 - 12 * q^61 - 100 * q^64 - 8 * q^71 - 56 * q^74 - 60 * q^76 + 64 * q^79 + 2 * q^89 - 98 * q^91 + 50 * q^94

Decomposition of \(S_{2}^{\mathrm{new}}(1125, [\chi])\) 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
																		$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
1125.2.b.a	$1125$	$2$	1125.b	5.b	$2$	$4$	$4$	$8.983$	4.0.4400.1	None					125.2.a.c	$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q-\beta _{3}q^{2}+(-1-2\beta _{2})q^{4}+(\beta _{1}-\beta _{3})q^{7}+\cdots\)
1125.2.b.b	$1125$	$2$	1125.b	5.b	$2$	$4$	$4$	$8.983$	\(\Q(i, \sqrt{5})\)	None					375.2.a.a	$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+(\beta _{1}-\beta _{3})q^{2}+3\beta _{2}q^{4}+(\beta _{1}+3\beta _{3})q^{7}+\cdots\)
1125.2.b.c	$1125$	$2$	1125.b	5.b	$2$	$4$	$4$	$8.983$	\(\Q(\zeta_{10})\)	None		✓			1125.2.a.i	$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2^{2}$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta_{3} q^{2}+\beta_{2} q^{4}+(-\beta_{3}+2\beta_1)q^{7}+\cdots\)
1125.2.b.d	$1125$	$2$	1125.b	5.b	$2$	$4$	$4$	$8.983$	\(\Q(\zeta_{10})\)	None		✓			1125.2.a.i	$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2^{2}$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta_{3} q^{2}+\beta_{2} q^{4}+(\beta_{3}-2\beta_1)q^{7}+\cdots\)
1125.2.b.e	$1125$	$2$	1125.b	5.b	$2$	$4$	$4$	$8.983$	\(\Q(i, \sqrt{5})\)	None					375.2.a.b	$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta _{1}q^{2}+(1+\beta _{2})q^{4}-\beta _{1}q^{7}+(2\beta _{1}+\cdots)q^{8}+\cdots\)
1125.2.b.f	$1125$	$2$	1125.b	5.b	$2$	$4$	$4$	$8.983$	\(\Q(i, \sqrt{5})\)	None					125.2.a.a	$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta _{1}q^{2}+(1+\beta _{2})q^{4}+3\beta _{3}q^{7}+(2\beta _{1}+\cdots)q^{8}+\cdots\)
1125.2.b.g	$1125$	$2$	1125.b	5.b	$2$	$8$	$8$	$8.983$	8.0.1632160000.5	None					375.2.a.e	$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+(\beta _{4}+\beta _{7})q^{2}+(-1+\beta _{2}+\beta _{5}+\beta _{6}+\cdots)q^{4}+\cdots\)
1125.2.b.h	$1125$	$2$	1125.b	5.b	$2$	$8$	$8$	$8.983$	8.0.324000000.1	\(\Q(\sqrt{-15}) \)		✓			1125.2.a.g	$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$5^{5}$	$\mathrm{U}(1)[D_{2}]$	\(q-\beta _{1}q^{2}+(-2+\beta _{2})q^{4}+(2\beta _{1}+\beta _{7})q^{8}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(1125, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(1125, [\chi]) \simeq \) \(S_{2}^{\mathrm{new}}(45, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(75, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(125, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(225, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(375, [\chi])\)\(^{\oplus 2}\)