Space of modular forms of level 374, weight 2, and Character 374.g

• Label: 374.2.g
• Level: $374$
• Weight: $2$
• Character orbit: 374.g
• Rep. character: $\chi_{374}(69,\cdot)$
• Character field: $\Q(\zeta_{5})$
• Dimension: $64$
• Newform subspaces: $7$
• Sturm bound: $108$
• Trace bound: $3$

Defining parameters

Level:	\( N \)	\(=\)	\( 374 = 2 \cdot 11 \cdot 17 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	374.g (of order \(5\) and degree \(4\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 11 \)
Character field:			\(\Q(\zeta_{5})\)
Newform subspaces:			\( 7 \)
Sturm bound:			\(108\)
Trace bound:			\(3\)
Distinguishing \(T_p\):			\(3\), \(5\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(374, [\chi])\).

	Total	New	Old
Modular forms	232	64	168
Cusp forms	200	64	136
Eisenstein series	32	0	32

Trace form

64 * q + 4 * q^3 - 16 * q^4 + 4 * q^5 + 4 * q^6 + 8 * q^7 - 12 * q^9 - 8 * q^10 + 4 * q^11 - 16 * q^12 + 8 * q^13 - 12 * q^14 + 4 * q^15 - 16 * q^16 + 4 * q^17 + 8 * q^18 + 16 * q^19 + 4 * q^20 + 8 * q^21 + 4 * q^22 - 32 * q^23 + 4 * q^24 - 8 * q^25 + 40 * q^27 - 12 * q^28 - 24 * q^29 - 36 * q^30 + 4 * q^31 - 44 * q^33 - 28 * q^35 - 12 * q^36 + 36 * q^37 - 32 * q^38 + 4 * q^39 - 8 * q^40 + 28 * q^41 + 8 * q^42 - 32 * q^43 + 4 * q^44 + 16 * q^45 + 16 * q^46 + 16 * q^47 + 4 * q^48 - 16 * q^49 + 8 * q^50 + 4 * q^51 - 12 * q^52 - 40 * q^54 + 60 * q^55 + 8 * q^56 + 24 * q^57 - 28 * q^58 + 20 * q^59 + 4 * q^60 - 12 * q^61 + 16 * q^62 + 64 * q^63 - 16 * q^64 - 80 * q^65 - 20 * q^66 - 56 * q^67 + 4 * q^68 - 64 * q^69 - 16 * q^70 + 16 * q^71 - 12 * q^72 - 40 * q^73 + 36 * q^74 + 12 * q^75 + 16 * q^76 + 36 * q^77 + 96 * q^78 + 32 * q^79 + 4 * q^80 - 60 * q^81 + 8 * q^82 - 8 * q^83 - 12 * q^84 + 12 * q^85 - 24 * q^86 - 8 * q^87 + 4 * q^88 - 24 * q^90 + 48 * q^91 + 8 * q^92 + 32 * q^93 - 52 * q^94 - 32 * q^95 + 4 * q^96 + 20 * q^97 + 56 * q^98 + 24 * q^99

Decomposition of \(S_{2}^{\mathrm{new}}(374, [\chi])\) 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
																		$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
374.2.g.a	$374$	$2$	374.g	11.c	$5$	$4$	$1$	$2.986$	\(\Q(\zeta_{10})\)	None		✓			374.2.g.a	$2$	$0$	\(-1\)	\(-4\)	\(7\)	\(-6\)	$1$	$\mathrm{SU}(2)[C_{5}]$	\(q+(-1+\zeta_{10}-\zeta_{10}^{2}+\zeta_{10}^{3})q^{2}+\cdots\)
374.2.g.b	$374$	$2$	374.g	11.c	$5$	$4$	$1$	$2.986$	\(\Q(\zeta_{10})\)	None		✓			374.2.g.b	$2$	$0$	\(-1\)	\(-2\)	\(-1\)	\(4\)	$1$	$\mathrm{SU}(2)[C_{5}]$	\(q+(-1+\zeta_{10}-\zeta_{10}^{2}+\zeta_{10}^{3})q^{2}+\cdots\)
374.2.g.c	$374$	$2$	374.g	11.c	$5$	$4$	$1$	$2.986$	\(\Q(\zeta_{10})\)	None		✓			374.2.g.c	$2$	$0$	\(1\)	\(-2\)	\(-5\)	\(2\)	$1$	$\mathrm{SU}(2)[C_{5}]$	\(q+(1-\zeta_{10}+\zeta_{10}^{2}-\zeta_{10}^{3})q^{2}+(-\zeta_{10}+\cdots)q^{3}+\cdots\)
374.2.g.d	$374$	$2$	374.g	11.c	$5$	$8$	$2$	$2.986$	8.0.13140625.1	None		✓			374.2.g.d	$2$	$0$	\(-2\)	\(5\)	\(3\)	\(-2\)	$1$	$\mathrm{SU}(2)[C_{5}]$	\(q-\beta _{3}q^{2}+(1-\beta _{2}-\beta _{3}+\beta _{6})q^{3}+\beta _{4}q^{4}+\cdots\)
374.2.g.e	$374$	$2$	374.g	11.c	$5$	$8$	$2$	$2.986$	8.0.159390625.1	None		✓			374.2.g.e	$2$	$0$	\(2\)	\(3\)	\(1\)	\(2\)	$1$	$\mathrm{SU}(2)[C_{5}]$	\(q+\beta _{6}q^{2}+(1-\beta _{5}-\beta _{6})q^{3}-\beta _{3}q^{4}+\cdots\)
374.2.g.f	$374$	$2$	374.g	11.c	$5$	$16$	$4$	$2.986$	\(\mathbb{Q}[x]/(x^{16} - \cdots)\)	None		✓			374.2.g.f	$2$	$0$	\(-4\)	\(5\)	\(-1\)	\(2\)	$1$	$\mathrm{SU}(2)[C_{5}]$	\(q+(-1+\beta _{3}-\beta _{6}-\beta _{8})q^{2}+(-\beta _{6}+\cdots)q^{3}+\cdots\)
374.2.g.g	$374$	$2$	374.g	11.c	$5$	$20$	$5$	$2.986$	\(\mathbb{Q}[x]/(x^{20} - \cdots)\)	None		✓	✓		374.2.g.g	$2$	$0$	\(5\)	\(-1\)	\(0\)	\(6\)	$5$	$\mathrm{SU}(2)[C_{5}]$	\(q+(1+\beta _{3}-\beta _{7}-\beta _{9})q^{2}-\beta _{5}q^{3}-\beta _{7}q^{4}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(374, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(374, [\chi]) \simeq \) \(S_{2}^{\mathrm{new}}(22, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(187, [\chi])\)\(^{\oplus 2}\)