Space of modular forms of level 375, weight 2, and Character 375.g

• Label: 375.2.g
• Level: $375$
• Weight: $2$
• Character orbit: 375.g
• Rep. character: $\chi_{375}(76,\cdot)$
• Character field: $\Q(\zeta_{5})$
• Dimension: $56$
• Newform subspaces: $5$
• Sturm bound: $100$
• Trace bound: $2$

Defining parameters

Level:	\( N \)	\(=\)	\( 375 = 3 \cdot 5^{3} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	375.g (of order \(5\) and degree \(4\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 25 \)
Character field:			\(\Q(\zeta_{5})\)
Newform subspaces:			\( 5 \)
Sturm bound:			\(100\)
Trace bound:			\(2\)
Distinguishing \(T_p\):			\(2\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(375, [\chi])\).

	Total	New	Old
Modular forms	240	56	184
Cusp forms	160	56	104
Eisenstein series	80	0	80

Trace form

56 * q + 2 * q^2 - 12 * q^4 + 2 * q^6 + 8 * q^7 - 12 * q^8 - 14 * q^9 - 6 * q^11 + 8 * q^12 + 12 * q^13 + 12 * q^14 - 20 * q^16 + 10 * q^17 - 8 * q^18 + 2 * q^19 + 4 * q^21 - 30 * q^22 - 36 * q^23 - 24 * q^24 - 8 * q^26 + 26 * q^28 - 36 * q^29 + 6 * q^31 - 12 * q^32 + 6 * q^33 + 66 * q^34 - 12 * q^36 + 8 * q^37 + 26 * q^38 + 8 * q^39 - 34 * q^41 + 14 * q^42 - 32 * q^43 - 26 * q^44 + 16 * q^46 + 16 * q^47 + 32 * q^48 + 40 * q^49 - 32 * q^51 - 40 * q^52 - 36 * q^53 + 2 * q^54 + 16 * q^57 - 38 * q^58 - 12 * q^59 - 20 * q^61 - 14 * q^62 - 2 * q^63 - 18 * q^64 + 16 * q^66 + 124 * q^68 + 12 * q^69 - 8 * q^71 - 12 * q^72 + 24 * q^73 + 32 * q^74 - 32 * q^76 + 56 * q^77 + 40 * q^78 + 20 * q^79 - 14 * q^81 - 4 * q^82 + 26 * q^83 - 12 * q^84 - 36 * q^86 - 8 * q^87 - 72 * q^88 + 12 * q^89 + 26 * q^91 - 22 * q^92 - 88 * q^93 + 18 * q^94 - 46 * q^96 - 42 * q^98 + 4 * q^99

Decomposition of \(S_{2}^{\mathrm{new}}(375, [\chi])\) 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
																		$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
375.2.g.a	$375$	$2$	375.g	25.d	$5$	$4$	$1$	$2.994$	\(\Q(\zeta_{10})\)	None					75.2.g.a	$2$	$0$	\(1\)	\(1\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{5}]$	\(q+(1-\zeta_{10}+\zeta_{10}^{2}-\zeta_{10}^{3})q^{2}+\zeta_{10}^{3}q^{3}+\cdots\)
375.2.g.b	$375$	$2$	375.g	25.d	$5$	$8$	$2$	$2.994$	8.0.26265625.1	None					75.2.g.b	$2$	$0$	\(1\)	\(2\)	\(0\)	\(-4\)	$5$	$\mathrm{SU}(2)[C_{5}]$	\(q+(\beta _{3}+\beta _{7})q^{2}+(1-\beta _{1}-\beta _{3}-\beta _{6}+\cdots)q^{3}+\cdots\)
375.2.g.c	$375$	$2$	375.g	25.d	$5$	$12$	$3$	$2.994$	\(\mathbb{Q}[x]/(x^{12} + \cdots)\)	None					75.2.g.c	$2$	$0$	\(0\)	\(-3\)	\(0\)	\(12\)	$5$	$\mathrm{SU}(2)[C_{5}]$	\(q-\beta _{2}q^{2}+\beta _{8}q^{3}+(-1-\beta _{4}+\beta _{8}+\cdots)q^{4}+\cdots\)
375.2.g.d	$375$	$2$	375.g	25.d	$5$	$16$	$4$	$2.994$	\(\mathbb{Q}[x]/(x^{16} + \cdots)\)	None					75.2.i.a	$2$	$0$	\(-2\)	\(4\)	\(0\)	\(16\)	$5^{2}$	$\mathrm{SU}(2)[C_{5}]$	\(q+\beta _{5}q^{2}+\beta _{3}q^{3}+(\beta _{8}-\beta _{11})q^{4}+(1+\cdots)q^{6}+\cdots\)
375.2.g.e	$375$	$2$	375.g	25.d	$5$	$16$	$4$	$2.994$	\(\mathbb{Q}[x]/(x^{16} + \cdots)\)	None					75.2.i.a	$2$	$0$	\(2\)	\(-4\)	\(0\)	\(-16\)	$5^{2}$	$\mathrm{SU}(2)[C_{5}]$	\(q-\beta _{5}q^{2}-\beta _{3}q^{3}+(\beta _{8}-\beta _{11})q^{4}+(1+\cdots)q^{6}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(375, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(375, [\chi]) \simeq \) \(S_{2}^{\mathrm{new}}(25, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(75, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(125, [\chi])\)\(^{\oplus 2}\)