Space of modular forms of level 912, weight 2, and Character 912.bn

• Label: 912.2.bn
• Level: $912$
• Weight: $2$
• Character orbit: 912.bn
• Rep. character: $\chi_{912}(65,\cdot)$
• Character field: $\Q(\zeta_{6})$
• Dimension: $76$
• Newform subspaces: $15$
• Sturm bound: $320$
• Trace bound: $7$

Defining parameters

Level:	\( N \)	\(=\)	\( 912 = 2^{4} \cdot 3 \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	912.bn (of order \(6\) and degree \(2\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 57 \)
Character field:			\(\Q(\zeta_{6})\)
Newform subspaces:			\( 15 \)
Sturm bound:			\(320\)
Trace bound:			\(7\)
Distinguishing \(T_p\):			\(5\), \(7\), \(17\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(912, [\chi])\).

	Total	New	Old
Modular forms	344	84	260
Cusp forms	296	76	220
Eisenstein series	48	8	40

Trace form

\( 76 q + 3 q^{3} + 4 q^{7} + q^{9} + O(q^{10}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(912, [\chi])\) into newform subspaces

Label	Level	Weight	Char	Prim	Char order	Dim	Rel. Dim	$A$	Field	CM	Self-dual	Inner twists	Rank*	Traces				Coefficient ring index	Sato-Tate	$q$-expansion
														$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
912.2.bn.a	$912$	$2$	912.bn	57.f	$6$	$2$	$1$	$7.282$	\(\Q(\sqrt{-3}) \)	\(\Q(\sqrt{-3}) \)		$4$	$0$	\(0\)	\(-3\)	\(0\)	\(-2\)	$1$	$\mathrm{U}(1)[D_{6}]$	\(q+(-1-\zeta_{6})q^{3}-q^{7}+3\zeta_{6}q^{9}+(2+\cdots)q^{13}+\cdots\)
912.2.bn.b	$912$	$2$	912.bn	57.f	$6$	$2$	$1$	$7.282$	\(\Q(\sqrt{-3}) \)	None		$2$	$0$	\(0\)	\(0\)	\(6\)	\(4\)	$1$	$\mathrm{SU}(2)[C_{6}]$	\(q+(-1+2\zeta_{6})q^{3}+(2+2\zeta_{6})q^{5}+2q^{7}+\cdots\)
912.2.bn.c	$912$	$2$	912.bn	57.f	$6$	$2$	$1$	$7.282$	\(\Q(\sqrt{-3}) \)	None		$2$	$0$	\(0\)	\(3\)	\(-6\)	\(-2\)	$1$	$\mathrm{SU}(2)[C_{6}]$	\(q+(1+\zeta_{6})q^{3}+(-2-2\zeta_{6})q^{5}-q^{7}+\cdots\)
912.2.bn.d	$912$	$2$	912.bn	57.f	$6$	$2$	$1$	$7.282$	\(\Q(\sqrt{-3}) \)	None		$2$	$0$	\(0\)	\(3\)	\(-6\)	\(4\)	$1$	$\mathrm{SU}(2)[C_{6}]$	\(q+(2-\zeta_{6})q^{3}+(-2-2\zeta_{6})q^{5}+2q^{7}+\cdots\)
912.2.bn.e	$912$	$2$	912.bn	57.f	$6$	$2$	$1$	$7.282$	\(\Q(\sqrt{-3}) \)	\(\Q(\sqrt{-3}) \)		$4$	$0$	\(0\)	\(3\)	\(0\)	\(10\)	$1$	$\mathrm{U}(1)[D_{6}]$	\(q+(1+\zeta_{6})q^{3}+5q^{7}+3\zeta_{6}q^{9}+(-6+\cdots)q^{13}+\cdots\)
912.2.bn.f	$912$	$2$	912.bn	57.f	$6$	$2$	$1$	$7.282$	\(\Q(\sqrt{-3}) \)	None		$2$	$0$	\(0\)	\(3\)	\(6\)	\(-2\)	$1$	$\mathrm{SU}(2)[C_{6}]$	\(q+(1+\zeta_{6})q^{3}+(2+2\zeta_{6})q^{5}-q^{7}+3\zeta_{6}q^{9}+\cdots\)
912.2.bn.g	$912$	$2$	912.bn	57.f	$6$	$4$	$2$	$7.282$	\(\Q(\sqrt{-2}, \sqrt{-3})\)	None		$2$	$0$	\(0\)	\(-4\)	\(0\)	\(-8\)	$1$	$\mathrm{SU}(2)[C_{6}]$	\(q+(-1-\beta _{3})q^{3}+\beta _{1}q^{5}+(-2+2\beta _{1}+\cdots)q^{7}+\cdots\)
912.2.bn.h	$912$	$2$	912.bn	57.f	$6$	$4$	$2$	$7.282$	\(\Q(\sqrt{-2}, \sqrt{-3})\)	None		$2$	$0$	\(0\)	\(-2\)	\(0\)	\(-8\)	$1$	$\mathrm{SU}(2)[C_{6}]$	\(q+(\beta _{1}-\beta _{2}-\beta _{3})q^{3}+\beta _{1}q^{5}+(-2+\cdots)q^{7}+\cdots\)
912.2.bn.i	$912$	$2$	912.bn	57.f	$6$	$4$	$2$	$7.282$	\(\Q(\sqrt{-3}, \sqrt{-11})\)	None		$2$	$0$	\(0\)	\(-2\)	\(3\)	\(-2\)	$1$	$\mathrm{SU}(2)[C_{6}]$	\(q+(-1+\beta _{1}-\beta _{3})q^{3}+(1-\beta _{1})q^{5}+\cdots\)
912.2.bn.j	$912$	$2$	912.bn	57.f	$6$	$4$	$2$	$7.282$	\(\Q(\sqrt{-3}, \sqrt{-11})\)	None		$2$	$0$	\(0\)	\(-1\)	\(-3\)	\(-2\)	$1$	$\mathrm{SU}(2)[C_{6}]$	\(q-\beta _{1}q^{3}+(-1-\beta _{3})q^{5}+(-\beta _{1}-\beta _{2}+\cdots)q^{7}+\cdots\)
912.2.bn.k	$912$	$2$	912.bn	57.f	$6$	$4$	$2$	$7.282$	\(\Q(\sqrt{-3}, \sqrt{-11})\)	None		$2$	$0$	\(0\)	\(1\)	\(-9\)	\(-2\)	$1$	$\mathrm{SU}(2)[C_{6}]$	\(q+(\beta _{2}+\beta _{3})q^{3}+(-2+\beta _{1}-\beta _{2})q^{5}+\cdots\)
912.2.bn.l	$912$	$2$	912.bn	57.f	$6$	$4$	$2$	$7.282$	\(\Q(\sqrt{-3}, \sqrt{-11})\)	None		$2$	$0$	\(0\)	\(2\)	\(9\)	\(-2\)	$1$	$\mathrm{SU}(2)[C_{6}]$	\(q+(\beta _{1}-\beta _{3})q^{3}+(2-\beta _{1}+\beta _{2})q^{5}+(-\beta _{1}+\cdots)q^{7}+\cdots\)
912.2.bn.m	$912$	$2$	912.bn	57.f	$6$	$8$	$4$	$7.282$	\(\Q(\zeta_{24})\)	None		$4$	$0$	\(0\)	\(0\)	\(0\)	\(16\)	$2^{2}$	$\mathrm{SU}(2)[C_{6}]$	\(q+(\zeta_{24}-\zeta_{24}^{3}-\zeta_{24}^{4})q^{3}-\zeta_{24}^{5}q^{5}+\cdots\)
912.2.bn.n	$912$	$2$	912.bn	57.f	$6$	$16$	$8$	$7.282$	\(\mathbb{Q}[x]/(x^{16} - \cdots)\)	None		$2$	$0$	\(0\)	\(-1\)	\(3\)	\(0\)	$2^{2}$	$\mathrm{SU}(2)[C_{6}]$	\(q-\beta _{4}q^{3}+(-\beta _{11}+\beta _{14})q^{5}+(-\beta _{5}+\cdots)q^{7}+\cdots\)
912.2.bn.o	$912$	$2$	912.bn	57.f	$6$	$16$	$8$	$7.282$	\(\mathbb{Q}[x]/(x^{16} - \cdots)\)	None		$2$	$0$	\(0\)	\(1\)	\(-3\)	\(0\)	$2^{2}$	$\mathrm{SU}(2)[C_{6}]$	\(q+\beta _{7}q^{3}+(\beta _{11}-\beta _{14})q^{5}+(-\beta _{5}+\beta _{13}+\cdots)q^{7}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(912, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(912, [\chi]) \cong \)