Space of modular forms of level 2312, weight 2, and Character 2312.b

• Label: 2312.2.b
• Level: $2312$
• Weight: $2$
• Character orbit: 2312.b
• Rep. character: $\chi_{2312}(577,\cdot)$
• Character field: $\Q$
• Dimension: $68$
• Newform subspaces: $15$
• Sturm bound: $612$
• Trace bound: $15$

Defining parameters

Level:	\( N \)	\(=\)	\( 2312 = 2^{3} \cdot 17^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	2312.b (of order \(2\) and degree \(1\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 17 \)
Character field:			\(\Q\)
Newform subspaces:			\( 15 \)
Sturm bound:			\(612\)
Trace bound:			\(15\)
Distinguishing \(T_p\):			\(3\), \(5\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(2312, [\chi])\).

	Total	New	Old
Modular forms	342	68	274
Cusp forms	270	68	202
Eisenstein series	72	0	72

Trace form

68 * q - 76 * q^9 + 12 * q^21 - 76 * q^25 + 12 * q^33 + 20 * q^35 + 12 * q^43 - 76 * q^49 + 4 * q^53 - 44 * q^55 + 12 * q^59 - 44 * q^67 - 36 * q^69 - 12 * q^77 + 80 * q^81 + 12 * q^83 - 20 * q^87 + 36 * q^89 - 12 * q^93

Decomposition of \(S_{2}^{\mathrm{new}}(2312, [\chi])\) 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
																		$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
2312.2.b.a	$2312$	$2$	2312.b	17.b	$2$	$2$	$2$	$18.461$	\(\Q(\sqrt{-2}) \)	None					136.2.k.d	$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+2\beta q^{3}+\beta q^{5}+2\beta q^{7}-5q^{9}+2\beta q^{11}+\cdots\)
2312.2.b.b	$2312$	$2$	2312.b	17.b	$2$	$2$	$2$	$18.461$	\(\Q(\sqrt{-1}) \)	None					136.2.a.b	$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta q^{3}-q^{9}-\beta q^{11}-6 q^{13}-4 q^{19}+\cdots\)
2312.2.b.c	$2312$	$2$	2312.b	17.b	$2$	$2$	$2$	$18.461$	\(\Q(\sqrt{-1}) \)	None					136.2.a.a	$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta q^{3}+\beta q^{5}-\beta q^{7}-q^{9}-3\beta q^{11}+\cdots\)
2312.2.b.d	$2312$	$2$	2312.b	17.b	$2$	$2$	$2$	$18.461$	\(\Q(\sqrt{-2}) \)	None					136.2.k.b	$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta q^{3}+2\beta q^{5}-2\beta q^{7}+q^{9}+\beta q^{11}+\cdots\)
2312.2.b.e	$2312$	$2$	2312.b	17.b	$2$	$2$	$2$	$18.461$	\(\Q(\sqrt{-2}) \)	None					136.2.k.c	$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta q^{3}-\beta q^{5}-\beta q^{7}+q^{9}+\beta q^{11}+\cdots\)
2312.2.b.f	$2312$	$2$	2312.b	17.b	$2$	$2$	$2$	$18.461$	\(\Q(\sqrt{-2}) \)	None					136.2.k.a	$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta q^{3}-3\beta q^{5}+3\beta q^{7}+q^{9}+\beta q^{11}+\cdots\)
2312.2.b.g	$2312$	$2$	2312.b	17.b	$2$	$4$	$4$	$18.461$	\(\Q(i, \sqrt{5})\)	None					136.2.a.c	$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2^{4}$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta _{1}q^{3}+\beta _{2}q^{5}+\beta _{1}q^{7}+(-3+\beta _{3})q^{9}+\cdots\)
2312.2.b.h	$2312$	$2$	2312.b	17.b	$2$	$4$	$4$	$18.461$	\(\Q(i, \sqrt{13})\)	None		✓			2312.2.a.e	$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+(\beta _{1}-\beta _{2})q^{3}-\beta _{1}q^{5}+\beta _{1}q^{7}+(-4+\cdots)q^{9}+\cdots\)
2312.2.b.i	$2312$	$2$	2312.b	17.b	$2$	$4$	$4$	$18.461$	4.0.2048.2	None					136.2.n.b	$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+(\beta _{1}+\beta _{3})q^{3}+(\beta _{1}-2\beta _{3})q^{5}+(\beta _{1}+\cdots)q^{7}+\cdots\)
2312.2.b.j	$2312$	$2$	2312.b	17.b	$2$	$4$	$4$	$18.461$	4.0.2048.2	None					136.2.n.a	$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta _{1}q^{3}-\beta _{3}q^{5}+(2\beta _{1}-\beta _{3})q^{7}+(1+\cdots)q^{9}+\cdots\)
2312.2.b.k	$2312$	$2$	2312.b	17.b	$2$	$4$	$4$	$18.461$	\(\Q(i, \sqrt{5})\)	None		✓			2312.2.a.f	$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta _{1}q^{3}+(3\beta _{1}+\beta _{3})q^{5}+(\beta _{1}+3\beta _{3})q^{7}+\cdots\)
2312.2.b.l	$2312$	$2$	2312.b	17.b	$2$	$6$	$6$	$18.461$	6.0.419904.1	None		✓			2312.2.a.o	$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+(\beta _{1}-\beta _{3}-\beta _{5})q^{3}+(\beta _{1}-2\beta _{3})q^{5}+\cdots\)
2312.2.b.m	$2312$	$2$	2312.b	17.b	$2$	$6$	$6$	$18.461$	6.0.419904.1	None		✓			2312.2.a.p	$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+(\beta _{1}+\beta _{3}+\beta _{5})q^{3}+(-\beta _{1}-2\beta _{3}+\cdots)q^{5}+\cdots\)
2312.2.b.n	$2312$	$2$	2312.b	17.b	$2$	$12$	$12$	$18.461$	\(\mathbb{Q}[x]/(x^{12} + \cdots)\)	None					136.2.n.c	$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2^{2}$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta _{1}q^{3}+\beta _{10}q^{5}+\beta _{6}q^{7}+(-2+\beta _{3}+\cdots)q^{9}+\cdots\)
2312.2.b.o	$2312$	$2$	2312.b	17.b	$2$	$12$	$12$	$18.461$	\(\mathbb{Q}[x]/(x^{12} + \cdots)\)	None		✓			2312.2.a.u	$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta _{1}q^{3}+(-\beta _{1}-\beta _{3}-\beta _{4}-\beta _{7}-\beta _{10}+\cdots)q^{5}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(2312, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(2312, [\chi]) \simeq \) \(S_{2}^{\mathrm{new}}(34, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(68, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(136, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(289, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(578, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(1156, [\chi])\)\(^{\oplus 2}\)