Space of modular forms of level 304, weight 2, and Character 304.u

• Label: 304.2.u
• Level: $304$
• Weight: $2$
• Character orbit: 304.u
• Rep. character: $\chi_{304}(17,\cdot)$
• Character field: $\Q(\zeta_{9})$
• Dimension: $54$
• Newform subspaces: $6$
• Sturm bound: $80$
• Trace bound: $5$

Defining parameters

Level:	\( N \)	\(=\)	\( 304 = 2^{4} \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	304.u (of order \(9\) and degree \(6\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 19 \)
Character field:			\(\Q(\zeta_{9})\)
Newform subspaces:			\( 6 \)
Sturm bound:			\(80\)
Trace bound:			\(5\)
Distinguishing \(T_p\):			\(3\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(304, [\chi])\).

	Total	New	Old
Modular forms	276	66	210
Cusp forms	204	54	150
Eisenstein series	72	12	60

Trace form

54 * q + 6 * q^3 - 6 * q^5 + 3 * q^7 - 12 * q^9 + 3 * q^11 - 6 * q^13 + 6 * q^15 - 6 * q^17 + 12 * q^19 + 3 * q^21 + 6 * q^23 - 6 * q^25 + 27 * q^27 - 6 * q^29 - 15 * q^31 - 3 * q^33 - 9 * q^35 - 12 * q^37 + 12 * q^39 - 12 * q^41 + 30 * q^43 - 3 * q^45 - 12 * q^47 - 12 * q^49 - 6 * q^51 - 18 * q^53 + 27 * q^55 - 6 * q^57 + 6 * q^59 - 18 * q^61 - 9 * q^63 + 9 * q^65 - 60 * q^67 - 27 * q^69 - 30 * q^71 + 42 * q^73 - 156 * q^75 + 30 * q^77 - 78 * q^79 + 45 * q^81 + 3 * q^83 - 78 * q^85 - 33 * q^87 + 6 * q^89 - 63 * q^91 + 3 * q^93 + 30 * q^95 - 36 * q^97 - 21 * q^99

Decomposition of \(S_{2}^{\mathrm{new}}(304, [\chi])\) 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
																		$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
304.2.u.a	$304$	$2$	304.u	19.e	$9$	$6$	$1$	$2.427$	\(\Q(\zeta_{18})\)	None					152.2.q.b	$2$	$1$	\(0\)	\(-9\)	\(-6\)	\(-6\)	$1$	$\mathrm{SU}(2)[C_{9}]$	\(q+(-1+\zeta_{18}-2\zeta_{18}^{2}-\zeta_{18}^{3}+\zeta_{18}^{5})q^{3}+\cdots\)
304.2.u.b	$304$	$2$	304.u	19.e	$9$	$6$	$1$	$2.427$	\(\Q(\zeta_{18})\)	None					19.2.e.a	$2$	$0$	\(0\)	\(3\)	\(-6\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{9}]$	\(q+(1-\zeta_{18}-\zeta_{18}^{3}+\zeta_{18}^{5})q^{3}+(-1+\cdots)q^{5}+\cdots\)
304.2.u.c	$304$	$2$	304.u	19.e	$9$	$6$	$1$	$2.427$	\(\Q(\zeta_{18})\)	None					38.2.e.a	$2$	$0$	\(0\)	\(3\)	\(0\)	\(6\)	$1$	$\mathrm{SU}(2)[C_{9}]$	\(q+(\zeta_{18}^{2}+\zeta_{18}^{3}-\zeta_{18}^{5})q^{3}+2\zeta_{18}^{4}q^{5}+\cdots\)
304.2.u.d	$304$	$2$	304.u	19.e	$9$	$6$	$1$	$2.427$	\(\Q(\zeta_{18})\)	None					152.2.q.a	$2$	$0$	\(0\)	\(6\)	\(6\)	\(-3\)	$1$	$\mathrm{SU}(2)[C_{9}]$	\(q+(1+\zeta_{18}^{2})q^{3}+(1-\zeta_{18}^{2}+\zeta_{18}^{5})q^{5}+\cdots\)
304.2.u.e	$304$	$2$	304.u	19.e	$9$	$12$	$2$	$2.427$	\(\mathbb{Q}[x]/(x^{12} - \cdots)\)	None					76.2.i.a	$2$	$0$	\(0\)	\(3\)	\(0\)	\(-3\)	$1$	$\mathrm{SU}(2)[C_{9}]$	\(q+(1+\beta _{5}-\beta _{7}-\beta _{9}-\beta _{11})q^{3}+(\beta _{1}+\cdots)q^{5}+\cdots\)
304.2.u.f	$304$	$2$	304.u	19.e	$9$	$18$	$3$	$2.427$	\(\mathbb{Q}[x]/(x^{18} - \cdots)\)	None			✓		152.2.q.c	$2$	$0$	\(0\)	\(0\)	\(0\)	\(9\)	$1$	$\mathrm{SU}(2)[C_{9}]$	\(q+(-\beta _{2}+\beta _{4})q^{3}+(-\beta _{6}+\beta _{7}-\beta _{10}+\cdots)q^{5}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(304, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(304, [\chi]) \simeq \) \(S_{2}^{\mathrm{new}}(19, [\chi])\)\(^{\oplus 5}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(38, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(76, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(152, [\chi])\)\(^{\oplus 2}\)