Space of modular forms of level 27, weight 15, and Character 27.b

• Label: 27.15.b
• Level: $27$
• Weight: $15$
• Character orbit: 27.b
• Rep. character: $\chi_{27}(26,\cdot)$
• Character field: $\Q$
• Dimension: $19$
• Newform subspaces: $4$
• Sturm bound: $45$
• Trace bound: $4$

Defining parameters

Level:	\( N \)	\(=\)	\( 27 = 3^{3} \)
Weight:	\( k \)	\(=\)	\( 15 \)
Character orbit:	\([\chi]\)	\(=\)	27.b (of order \(2\) and degree \(1\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 3 \)
Character field:			\(\Q\)
Newform subspaces:			\( 4 \)
Sturm bound:			\(45\)
Trace bound:			\(4\)
Distinguishing \(T_p\):			\(2\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{15}(27, [\chi])\).

	Total	New	Old
Modular forms	45	19	26
Cusp forms	39	19	20
Eisenstein series	6	0	6

Trace form

19 * q - 170366 * q^4 + 93965 * q^7 - 19253502 * q^10 - 147980269 * q^13 + 725920234 * q^16 + 387979139 * q^19 + 8721888858 * q^22 - 27472229903 * q^25 + 41659798106 * q^28 + 68978528360 * q^31 - 243639534420 * q^34 + 371206250255 * q^37 + 582958838502 * q^40 - 790568790610 * q^43 - 118023181776 * q^46 - 473897922216 * q^49 + 7095379086320 * q^52 + 502283090430 * q^55 - 5879403539316 * q^58 + 3288248756951 * q^61 + 2244374430382 * q^64 - 1281918431305 * q^67 - 31971407836950 * q^70 + 11987889809537 * q^73 - 37612463892220 * q^76 - 47957055687913 * q^79 + 166237982911656 * q^82 + 36443589165468 * q^85 - 337578543476514 * q^88 + 203522825626033 * q^91 - 215052918151860 * q^94 - 130092231045667 * q^97

Decomposition of \(S_{15}^{\mathrm{new}}(27, [\chi])\) 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
																		$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
27.15.b.a	$27$	$15$	27.b	3.b	$2$	$1$	$1$	$33.569$	\(\Q\)	\(\Q(\sqrt{-3}) \)	✓	✓			27.15.b.a	$2$	$0$	\(0\)	\(0\)	\(0\)	\(1461083\)	$1$	$\mathrm{U}(1)[D_{2}]$	\(q+2^{14}q^{4}+1461083q^{7}+33388991q^{13}+\cdots\)
27.15.b.b	$27$	$15$	27.b	3.b	$2$	$4$	$4$	$33.569$	\(\mathbb{Q}[x]/(x^{4} + \cdots)\)	None		✓			27.15.b.b	$2$	$0$	\(0\)	\(0\)	\(0\)	\(-1064644\)	$2^{6}\cdot 3^{8}$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta _{1}q^{2}+(-18122+17\beta _{3})q^{4}+(312\beta _{1}+\cdots)q^{5}+\cdots\)
27.15.b.c	$27$	$15$	27.b	3.b	$2$	$4$	$4$	$33.569$	\(\mathbb{Q}[x]/(x^{4} + \cdots)\)	None		✓			27.15.b.c	$2$	$0$	\(0\)	\(0\)	\(0\)	\(448868\)	$2^{2}\cdot 3^{9}\cdot 5^{2}$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta _{1}q^{2}+(-5621+\beta _{3})q^{4}+(-149\beta _{1}+\cdots)q^{5}+\cdots\)
27.15.b.d	$27$	$15$	27.b	3.b	$2$	$10$	$10$	$33.569$	\(\mathbb{Q}[x]/(x^{10} + \cdots)\)	None		✓	✓		27.15.b.d	$2$	$0$	\(0\)	\(0\)	\(0\)	\(-751342\)	$2^{21}\cdot 3^{65}$	$\mathrm{SU}(2)[C_{2}]$	\(q-\beta _{5}q^{2}+(-9178-\beta _{1})q^{4}+(42\beta _{5}+\cdots)q^{5}+\cdots\)

Decomposition of \(S_{15}^{\mathrm{old}}(27, [\chi])\) into lower level spaces

\( S_{15}^{\mathrm{old}}(27, [\chi]) \simeq \) \(S_{15}^{\mathrm{new}}(3, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{15}^{\mathrm{new}}(9, [\chi])\)\(^{\oplus 2}\)