Space of modular forms of level 675, weight 2, and Character 675.l

• Label: 675.2.l
• Level: $675$
• Weight: $2$
• Character orbit: 675.l
• Rep. character: $\chi_{675}(76,\cdot)$
• Character field: $\Q(\zeta_{9})$
• Dimension: $324$
• Newform subspaces: $8$
• Sturm bound: $180$
• Trace bound: $2$

Defining parameters

Level:	\( N \)	\(=\)	\( 675 = 3^{3} \cdot 5^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	675.l (of order \(9\) and degree \(6\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 27 \)
Character field:			\(\Q(\zeta_{9})\)
Newform subspaces:			\( 8 \)
Sturm bound:			\(180\)
Trace bound:			\(2\)
Distinguishing \(T_p\):			\(2\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(675, [\chi])\).

	Total	New	Old
Modular forms	576	360	216
Cusp forms	504	324	180
Eisenstein series	72	36	36

Trace form

324 * q + 6 * q^2 + 6 * q^3 + 6 * q^4 - 24 * q^6 + 6 * q^7 + 12 * q^8 - 21 * q^11 + 24 * q^12 + 6 * q^13 + 15 * q^14 - 24 * q^16 + 15 * q^17 - 21 * q^18 + 3 * q^19 + 12 * q^21 + 15 * q^22 - 24 * q^23 + 12 * q^24 + 18 * q^26 - 21 * q^27 + 12 * q^28 - 30 * q^29 - 27 * q^31 - 72 * q^32 + 6 * q^33 + 33 * q^34 + 18 * q^36 + 3 * q^37 + 6 * q^38 - 33 * q^39 + 3 * q^41 - 78 * q^42 + 15 * q^43 - 3 * q^44 - 9 * q^46 - 57 * q^47 - 99 * q^48 - 12 * q^49 - 108 * q^51 + 45 * q^52 - 54 * q^53 + 90 * q^54 + 69 * q^56 - 27 * q^57 + 33 * q^58 - 42 * q^59 - 36 * q^61 - 6 * q^62 - 21 * q^63 - 96 * q^64 - 15 * q^66 + 33 * q^67 - 75 * q^68 + 93 * q^69 - 63 * q^71 + 126 * q^72 + 12 * q^73 + 111 * q^74 - 36 * q^76 + 75 * q^77 - 36 * q^78 + 42 * q^79 - 108 * q^81 + 12 * q^82 - 9 * q^83 - 12 * q^84 - 111 * q^86 + 57 * q^87 - 78 * q^88 - 87 * q^89 - 9 * q^92 + 21 * q^93 + 69 * q^94 - 264 * q^96 + 51 * q^97 + 75 * q^98 - 99 * q^99

Decomposition of \(S_{2}^{\mathrm{new}}(675, [\chi])\) 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
																		$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
675.2.l.a	$675$	$2$	675.l	27.e	$9$	$6$	$1$	$5.390$	\(\Q(\zeta_{18})\)	None		✓			675.2.l.a	$2$	$1$	\(-6\)	\(0\)	\(0\)	\(-6\)	$1$	$\mathrm{SU}(2)[C_{9}]$	\(q+(-1-\zeta_{18}+\zeta_{18}^{4}+\zeta_{18}^{5})q^{2}+\cdots\)
675.2.l.b	$675$	$2$	675.l	27.e	$9$	$6$	$1$	$5.390$	\(\Q(\zeta_{18})\)	None		✓			675.2.l.a	$2$	$0$	\(6\)	\(0\)	\(0\)	\(6\)	$1$	$\mathrm{SU}(2)[C_{9}]$	\(q+(1+\zeta_{18}-\zeta_{18}^{4}-\zeta_{18}^{5})q^{2}+(-\zeta_{18}^{2}+\cdots)q^{3}+\cdots\)
675.2.l.c	$675$	$2$	675.l	27.e	$9$	$12$	$2$	$5.390$	12.0.\(\cdots\).1	None					27.2.e.a	$2$	$0$	\(6\)	\(6\)	\(0\)	\(6\)	$3$	$\mathrm{SU}(2)[C_{9}]$	\(q+(1+\beta _{3}-\beta _{8})q^{2}+(1+\beta _{2}-\beta _{6}+\beta _{8}+\cdots)q^{3}+\cdots\)
675.2.l.d	$675$	$2$	675.l	27.e	$9$	$30$	$5$	$5.390$		None					135.2.k.a	$2$	$0$	\(0\)	\(-3\)	\(0\)	\(0\)		$\mathrm{SU}(2)[C_{9}]$
675.2.l.e	$675$	$2$	675.l	27.e	$9$	$42$	$7$	$5.390$		None					135.2.k.b	$2$	$0$	\(0\)	\(3\)	\(0\)	\(0\)		$\mathrm{SU}(2)[C_{9}]$
675.2.l.f	$675$	$2$	675.l	27.e	$9$	$66$	$11$	$5.390$		None		✓			675.2.l.f	$2$	$0$	\(-6\)	\(0\)	\(0\)	\(-6\)		$\mathrm{SU}(2)[C_{9}]$
675.2.l.g	$675$	$2$	675.l	27.e	$9$	$66$	$11$	$5.390$		None		✓			675.2.l.f	$2$	$0$	\(6\)	\(0\)	\(0\)	\(6\)		$\mathrm{SU}(2)[C_{9}]$
675.2.l.h	$675$	$2$	675.l	27.e	$9$	$96$	$16$	$5.390$		None			✓		135.2.p.a	$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)		$\mathrm{SU}(2)[C_{9}]$

Decomposition of \(S_{2}^{\mathrm{old}}(675, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(675, [\chi]) \simeq \) \(S_{2}^{\mathrm{new}}(27, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(135, [\chi])\)\(^{\oplus 2}\)