Space of modular forms of level 270, weight 11, and Character 270.h

• Label: 270.11.h
• Level: $270$
• Weight: $11$
• Character orbit: 270.h
• Rep. character: $\chi_{270}(71,\cdot)$
• Character field: $\Q(\zeta_{6})$
• Dimension: $80$
• Newform subspaces: $1$
• Sturm bound: $594$
• Trace bound: $0$

Defining parameters

Level:	\( N \)	\(=\)	\( 270 = 2 \cdot 3^{3} \cdot 5 \)
Weight:	\( k \)	\(=\)	\( 11 \)
Character orbit:	\([\chi]\)	\(=\)	270.h (of order \(6\) and degree \(2\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 9 \)
Character field:			\(\Q(\zeta_{6})\)
Newform subspaces:			\( 1 \)
Sturm bound:			\(594\)
Trace bound:			\(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{11}(270, [\chi])\).

	Total	New	Old
Modular forms	1104	80	1024
Cusp forms	1056	80	976
Eisenstein series	48	0	48

Trace form

80 * q + 20480 * q^4 - 24476 * q^7 - 1944 * q^11 + 561100 * q^13 + 175680 * q^14 - 10485760 * q^16 + 5932480 * q^19 - 6946944 * q^22 + 2008908 * q^23 + 78125000 * q^25 - 25063424 * q^28 + 54816192 * q^29 + 11191216 * q^31 - 61492992 * q^34 + 204029848 * q^37 + 247344768 * q^38 - 306039276 * q^41 + 173186188 * q^43 + 366913920 * q^46 + 1316963016 * q^47 - 1286128428 * q^49 - 287283200 * q^52 + 89948160 * q^56 - 5720414040 * q^59 - 1218762932 * q^61 - 10737418240 * q^64 + 2716312500 * q^65 + 1597633744 * q^67 - 1475831808 * q^68 + 183000000 * q^70 - 10426752656 * q^73 + 15538503168 * q^74 + 1518714880 * q^76 - 18397247724 * q^77 + 3046073392 * q^79 + 10345792512 * q^82 + 27645650316 * q^83 - 2312062500 * q^85 - 6643133568 * q^86 + 3556835328 * q^88 + 11114363408 * q^91 + 1028560896 * q^92 - 6416128320 * q^94 + 17922375000 * q^95 - 10980388424 * q^97

Decomposition of \(S_{11}^{\mathrm{new}}(270, [\chi])\) 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
																		$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
270.11.h.a	$270$	$11$	270.h	9.d	$6$	$80$	$40$	$171.546$		None			✓	✓	90.11.h.a	$2$	$0$	\(0\)	\(0\)	\(0\)	\(-24476\)		$\mathrm{SU}(2)[C_{6}]$

Decomposition of \(S_{11}^{\mathrm{old}}(270, [\chi])\) into lower level spaces

\( S_{11}^{\mathrm{old}}(270, [\chi]) \simeq \) \(S_{11}^{\mathrm{new}}(9, [\chi])\)\(^{\oplus 8}\)\(\oplus\)\(S_{11}^{\mathrm{new}}(18, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{11}^{\mathrm{new}}(27, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{11}^{\mathrm{new}}(45, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{11}^{\mathrm{new}}(54, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{11}^{\mathrm{new}}(90, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{11}^{\mathrm{new}}(135, [\chi])\)\(^{\oplus 2}\)