Space of modular forms of level 368, weight 2, and Character 368.m

• Label: 368.2.m
• Level: $368$
• Weight: $2$
• Character orbit: 368.m
• Rep. character: $\chi_{368}(49,\cdot)$
• Character field: $\Q(\zeta_{11})$
• Dimension: $110$
• Newform subspaces: $6$
• Sturm bound: $96$
• Trace bound: $3$

Defining parameters

Level:	\( N \)	\(=\)	\( 368 = 2^{4} \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	368.m (of order \(11\) and degree \(10\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 23 \)
Character field:			\(\Q(\zeta_{11})\)
Newform subspaces:			\( 6 \)
Sturm bound:			\(96\)
Trace bound:			\(3\)
Distinguishing \(T_p\):			\(3\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(368, [\chi])\).

	Total	New	Old
Modular forms	540	130	410
Cusp forms	420	110	310
Eisenstein series	120	20	100

Trace form

110 * q + 9 * q^3 - 9 * q^5 + 7 * q^7 - 18 * q^9 + 11 * q^11 - 9 * q^13 + 11 * q^15 - 9 * q^17 + 7 * q^19 - 11 * q^21 + 14 * q^23 - 16 * q^25 + 9 * q^27 - 9 * q^29 + q^31 - 3 * q^33 + 11 * q^35 - q^37 - 3 * q^39 - 17 * q^41 + 11 * q^43 - 12 * q^45 + 44 * q^47 - 22 * q^49 + 7 * q^51 - q^53 + 35 * q^55 - 19 * q^57 + 15 * q^59 + 7 * q^61 - 21 * q^63 - 23 * q^65 + 19 * q^67 - 11 * q^69 + 17 * q^71 - 9 * q^73 - 61 * q^75 - 47 * q^77 - 83 * q^79 + 74 * q^81 - 35 * q^83 + q^85 - 141 * q^87 + 27 * q^89 - 114 * q^91 - 166 * q^93 - 129 * q^95 + 27 * q^97 - 179 * q^99

Decomposition of \(S_{2}^{\mathrm{new}}(368, [\chi])\) 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
																		$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
368.2.m.a	$368$	$2$	368.m	23.c	$11$	$10$	$1$	$2.938$	\(\Q(\zeta_{22})\)	None					46.2.c.b	$2$	$0$	\(0\)	\(0\)	\(-4\)	\(7\)	$1$	$\mathrm{SU}(2)[C_{11}]$	\(q+(-\zeta_{22}^{3}-\zeta_{22}^{4}+\zeta_{22}^{5}+\zeta_{22}^{6}+\cdots)q^{3}+\cdots\)
368.2.m.b	$368$	$2$	368.m	23.c	$11$	$10$	$1$	$2.938$	\(\Q(\zeta_{22})\)	None					46.2.c.a	$2$	$0$	\(0\)	\(4\)	\(-6\)	\(-3\)	$1$	$\mathrm{SU}(2)[C_{11}]$	\(q+(\zeta_{22}^{3}-\zeta_{22}^{4}+\zeta_{22}^{5}-\zeta_{22}^{6})q^{3}+\cdots\)
368.2.m.c	$368$	$2$	368.m	23.c	$11$	$10$	$1$	$2.938$	\(\Q(\zeta_{22})\)	None					23.2.c.a	$2$	$0$	\(0\)	\(7\)	\(-3\)	\(5\)	$1$	$\mathrm{SU}(2)[C_{11}]$	\(q+(1+\zeta_{22}^{4}-\zeta_{22}^{5}-\zeta_{22}^{9})q^{3}+(-1+\cdots)q^{5}+\cdots\)
368.2.m.d	$368$	$2$	368.m	23.c	$11$	$20$	$2$	$2.938$	\(\mathbb{Q}[x]/(x^{20} - \cdots)\)	None					92.2.e.a	$2$	$0$	\(0\)	\(-2\)	\(2\)	\(-2\)	$1$	$\mathrm{SU}(2)[C_{11}]$	\(q+(-1+\beta _{6}-\beta _{8}+\beta _{9}+\beta _{10}+\beta _{11}+\cdots)q^{3}+\cdots\)
368.2.m.e	$368$	$2$	368.m	23.c	$11$	$30$	$3$	$2.938$		None					184.2.i.b	$2$	$0$	\(0\)	\(-2\)	\(0\)	\(13\)		$\mathrm{SU}(2)[C_{11}]$
368.2.m.f	$368$	$2$	368.m	23.c	$11$	$30$	$3$	$2.938$		None					184.2.i.a	$2$	$0$	\(0\)	\(2\)	\(2\)	\(-13\)		$\mathrm{SU}(2)[C_{11}]$

Decomposition of \(S_{2}^{\mathrm{old}}(368, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(368, [\chi]) \simeq \) \(S_{2}^{\mathrm{new}}(23, [\chi])\)\(^{\oplus 5}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(46, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(92, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(184, [\chi])\)\(^{\oplus 2}\)