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

• Label: 3150.2.bf
• Level: $3150$
• Weight: $2$
• Character orbit: 3150.bf
• Rep. character: $\chi_{3150}(1151,\cdot)$
• Character field: $\Q(\zeta_{6})$
• Dimension: $104$
• Newform subspaces: $6$
• 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.bf (of order \(6\) and degree \(2\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 21 \)
Character field:			\(\Q(\zeta_{6})\)
Newform subspaces:			\( 6 \)
Sturm bound:			\(1440\)
Trace bound:			\(11\)
Distinguishing \(T_p\):			\(11\), \(37\)

Dimensions

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

	Total	New	Old
Modular forms	1536	104	1432
Cusp forms	1344	104	1240
Eisenstein series	192	0	192

Trace form

104 * q + 52 * q^4 - 4 * q^7 - 52 * q^16 - 48 * q^19 + 24 * q^22 + 4 * q^28 + 12 * q^31 - 32 * q^37 - 16 * q^46 - 28 * q^49 + 20 * q^58 + 48 * q^61 - 104 * q^64 + 8 * q^67 - 24 * q^73 - 20 * q^79 - 48 * q^82 + 12 * q^88 + 16 * q^91 + 24 * q^94

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.bf.a	$3150$	$2$	3150.bf	21.g	$6$	$8$	$4$	$25.153$	\(\Q(\zeta_{24})\)	None					126.2.k.a	$4$	$0$	\(0\)	\(0\)	\(0\)	\(-4\)	$2^{2}\cdot 3^{2}$	$\mathrm{SU}(2)[C_{6}]$	\(q-\beta_1 q^{2}+\beta_{2} q^{4}+(-\beta_{7}+\beta_{4}-\beta_{2})q^{7}+\cdots\)
3150.2.bf.b	$3150$	$2$	3150.bf	21.g	$6$	$8$	$4$	$25.153$	\(\Q(\zeta_{24})\)	None					630.2.be.a	$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{6}]$	\(q+\zeta_{24}^{2}q^{2}+\zeta_{24}^{4}q^{4}+(\zeta_{24}-3\zeta_{24}^{5}+\cdots)q^{7}+\cdots\)
3150.2.bf.c	$3150$	$2$	3150.bf	21.g	$6$	$8$	$4$	$25.153$	\(\Q(\zeta_{24})\)	None					630.2.be.a	$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{6}]$	\(q-\zeta_{24}^{2}q^{2}+\zeta_{24}^{4}q^{4}+(-\zeta_{24}+3\zeta_{24}^{5}+\cdots)q^{7}+\cdots\)
3150.2.bf.d	$3150$	$2$	3150.bf	21.g	$6$	$24$	$12$	$25.153$		None		✓			3150.2.bf.d	$4$	$0$	\(0\)	\(0\)	\(0\)	\(-4\)		$\mathrm{SU}(2)[C_{6}]$
3150.2.bf.e	$3150$	$2$	3150.bf	21.g	$6$	$24$	$12$	$25.153$		None		✓			3150.2.bf.d	$4$	$0$	\(0\)	\(0\)	\(0\)	\(4\)		$\mathrm{SU}(2)[C_{6}]$
3150.2.bf.f	$3150$	$2$	3150.bf	21.g	$6$	$32$	$16$	$25.153$		None			✓		630.2.bo.a	$8$	$0$	\(0\)	\(0\)	\(0\)	\(0\)		$\mathrm{SU}(2)[C_{6}]$

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

\( S_{2}^{\mathrm{old}}(3150, [\chi]) \simeq \) \(S_{2}^{\mathrm{new}}(21, [\chi])\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(42, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(63, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(105, [\chi])\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(126, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(210, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(315, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(525, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(630, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(1050, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(1575, [\chi])\)\(^{\oplus 2}\)