Space of modular forms of level 2100, weight 3, and Character 2100.e

• Label: 2100.3.e
• Level: $2100$
• Weight: $3$
• Character orbit: 2100.e
• Rep. character: $\chi_{2100}(449,\cdot)$
• Character field: $\Q$
• Dimension: $72$
• Newform subspaces: $3$
• Sturm bound: $1440$
• Trace bound: $9$

Defining parameters

Level:	\( N \)	\(=\)	\( 2100 = 2^{2} \cdot 3 \cdot 5^{2} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	2100.e (of order \(2\) and degree \(1\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 15 \)
Character field:			\(\Q\)
Newform subspaces:			\( 3 \)
Sturm bound:			\(1440\)
Trace bound:			\(9\)
Distinguishing \(T_p\):			\(11\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{3}(2100, [\chi])\).

	Total	New	Old
Modular forms	996	72	924
Cusp forms	924	72	852
Eisenstein series	72	0	72

Trace form

\( 72 q + 24 q^{9} - 40 q^{19} - 28 q^{21} + 152 q^{31} + 20 q^{39} - 504 q^{49} - 304 q^{51} + 240 q^{61} - 244 q^{69} - 328 q^{79} - 336 q^{81} + 168 q^{91} + 480 q^{99}+O(q^{100}) \)

Decomposition of \(S_{3}^{\mathrm{new}}(2100, [\chi])\) 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
																		$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
2100.3.e.a	$2100$	$3$	2100.e	15.d	$2$	$8$	$8$	$57.221$	8.0.\(\cdots\).14	None					84.3.c.a	$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2^{4}$	$\mathrm{SU}(2)[C_{2}]$	\(q+(\beta _{1}-2\beta _{6})q^{3}+(-\beta _{1}-\beta _{5}+\beta _{6}+\cdots)q^{7}+\cdots\)
2100.3.e.b	$2100$	$3$	2100.e	15.d	$2$	$32$	$32$	$57.221$		None		✓			2100.3.g.b	$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)		$\mathrm{SU}(2)[C_{2}]$
2100.3.e.c	$2100$	$3$	2100.e	15.d	$2$	$32$	$32$	$57.221$		None					420.3.g.a	$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)		$\mathrm{SU}(2)[C_{2}]$

Decomposition of \(S_{3}^{\mathrm{old}}(2100, [\chi])\) into lower level spaces

\( S_{3}^{\mathrm{old}}(2100, [\chi]) \simeq \) \(S_{3}^{\mathrm{new}}(15, [\chi])\)\(^{\oplus 12}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(30, [\chi])\)\(^{\oplus 8}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(60, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(75, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(105, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(150, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(210, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(300, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(420, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(525, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(1050, [\chi])\)\(^{\oplus 2}\)