Space of modular forms of level 3150, weight 2, and Character 3150.bp

• Label: 3150.2.bp
• Level: $3150$
• Weight: $2$
• Character orbit: 3150.bp
• Rep. character: $\chi_{3150}(899,\cdot)$
• Character field: $\Q(\zeta_{6})$
• Dimension: $96$
• Newform subspaces: $8$
• Sturm bound: $1440$
• Trace bound: $11$

Defining parameters

Level:	\( N \)	\(=\)	\( 3150 = 2 \cdot 3^{2} \cdot 5^{2} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	3150.bp (of order \(6\) and degree \(2\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 105 \)
Character field:			\(\Q(\zeta_{6})\)
Newform subspaces:			\( 8 \)
Sturm bound:			\(1440\)
Trace bound:			\(11\)
Distinguishing \(T_p\):			\(11\), \(13\), \(17\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(3150, [\chi])\).

	Total	New	Old
Modular forms	1536	96	1440
Cusp forms	1344	96	1248
Eisenstein series	192	0	192

Trace form

\( 96 q - 48 q^{4} - 48 q^{16} + 24 q^{19} - 24 q^{31} + 16 q^{46} + 64 q^{49} + 24 q^{61} + 96 q^{64} + 32 q^{79} + 8 q^{91} + 144 q^{94}+O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(3150, [\chi])\) 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
																		$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
3150.2.bp.a	$3150$	$2$	3150.bp	105.p	$6$	$8$	$4$	$25.153$	\(\Q(\zeta_{24})\)	None					630.2.be.a	$2$	$0$	\(-4\)	\(0\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{6}]$	\(q+(-1+\zeta_{24}^{4})q^{2}-\zeta_{24}^{4}q^{4}+(3\zeta_{24}^{3}+\cdots)q^{7}+\cdots\)
3150.2.bp.b	$3150$	$2$	3150.bp	105.p	$6$	$8$	$4$	$25.153$	\(\Q(\zeta_{24})\)	None					126.2.k.a	$4$	$0$	\(-4\)	\(0\)	\(0\)	\(0\)	$2^{2}\cdot 3^{2}$	$\mathrm{SU}(2)[C_{6}]$	\(q+(\beta_{2}-1)q^{2}-\beta_{2} q^{4}+(-\beta_{5}+\beta_{3}-\beta_1)q^{7}+\cdots\)
3150.2.bp.c	$3150$	$2$	3150.bp	105.p	$6$	$8$	$4$	$25.153$	\(\Q(\zeta_{24})\)	None					630.2.be.a	$2$	$0$	\(-4\)	\(0\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{6}]$	\(q+(-1+\zeta_{24}^{4})q^{2}-\zeta_{24}^{4}q^{4}+(3\zeta_{24}^{3}+\cdots)q^{7}+\cdots\)
3150.2.bp.d	$3150$	$2$	3150.bp	105.p	$6$	$8$	$4$	$25.153$	\(\Q(\zeta_{24})\)	None					630.2.be.a	$2$	$0$	\(4\)	\(0\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{6}]$	\(q+(1-\zeta_{24}^{4})q^{2}-\zeta_{24}^{4}q^{4}+(-3\zeta_{24}^{3}+\cdots)q^{7}+\cdots\)
3150.2.bp.e	$3150$	$2$	3150.bp	105.p	$6$	$8$	$4$	$25.153$	\(\Q(\zeta_{24})\)	None					126.2.k.a	$4$	$0$	\(4\)	\(0\)	\(0\)	\(0\)	$2^{2}\cdot 3^{2}$	$\mathrm{SU}(2)[C_{6}]$	\(q+(-\beta_{2}+1)q^{2}-\beta_{2} q^{4}+(-\beta_{5}-\beta_{3}+\beta_1)q^{7}+\cdots\)
3150.2.bp.f	$3150$	$2$	3150.bp	105.p	$6$	$8$	$4$	$25.153$	\(\Q(\zeta_{24})\)	None					630.2.be.a	$2$	$0$	\(4\)	\(0\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{6}]$	\(q+(1-\zeta_{24}^{4})q^{2}-\zeta_{24}^{4}q^{4}+(-3\zeta_{24}^{3}+\cdots)q^{7}+\cdots\)
3150.2.bp.g	$3150$	$2$	3150.bp	105.p	$6$	$24$	$12$	$25.153$		None		✓			3150.2.bf.d	$4$	$0$	\(-12\)	\(0\)	\(0\)	\(0\)		$\mathrm{SU}(2)[C_{6}]$
3150.2.bp.h	$3150$	$2$	3150.bp	105.p	$6$	$24$	$12$	$25.153$		None		✓			3150.2.bf.d	$4$	$0$	\(12\)	\(0\)	\(0\)	\(0\)		$\mathrm{SU}(2)[C_{6}]$

Decomposition of \(S_{2}^{\mathrm{old}}(3150, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(3150, [\chi]) \simeq \) \(S_{2}^{\mathrm{new}}(105, [\chi])\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(210, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(315, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(525, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(630, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(1050, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(1575, [\chi])\)\(^{\oplus 2}\)