Space of modular forms of level 1800, weight 3, and Character 1800.c

• Label: 1800.3.c
• Level: $1800$
• Weight: $3$
• Character orbit: 1800.c
• Rep. character: $\chi_{1800}(449,\cdot)$
• Character field: $\Q$
• Dimension: $36$
• Newform subspaces: $5$
• Sturm bound: $1080$
• Trace bound: $19$

Defining parameters

Level:	\( N \)	\(=\)	\( 1800 = 2^{3} \cdot 3^{2} \cdot 5^{2} \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	1800.c (of order \(2\) and degree \(1\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 15 \)
Character field:			\(\Q\)
Newform subspaces:			\( 5 \)
Sturm bound:			\(1080\)
Trace bound:			\(19\)
Distinguishing \(T_p\):			\(7\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{3}(1800, [\chi])\).

	Total	New	Old
Modular forms	768	36	732
Cusp forms	672	36	636
Eisenstein series	96	0	96

Trace form

\( 36 q - 112 q^{31} - 492 q^{49} + 120 q^{61} + 208 q^{79} - 544 q^{91}+O(q^{100}) \)

Decomposition of \(S_{3}^{\mathrm{new}}(1800, [\chi])\) 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
																		$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
1800.3.c.a	$1800$	$3$	1800.c	15.d	$2$	$4$	$4$	$49.046$	\(\Q(\zeta_{8})\)	None					72.3.e.a	$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2^{2}$	$\mathrm{SU}(2)[C_{2}]$	\(q-6\beta_1 q^{7}-4\beta_{2} q^{11}-4\beta_1 q^{13}+\cdots\)
1800.3.c.b	$1800$	$3$	1800.c	15.d	$2$	$8$	$8$	$49.046$	8.0.40960000.1	None					360.3.l.a	$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2^{11}$	$\mathrm{SU}(2)[C_{2}]$	\(q+(4\beta _{1}-\beta _{5})q^{7}+(-\beta _{2}-3\beta _{4})q^{11}+\cdots\)
1800.3.c.c	$1800$	$3$	1800.c	15.d	$2$	$8$	$8$	$49.046$	8.0.8540717056.1	None		✓			1800.3.l.c	$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2^{10}$	$\mathrm{SU}(2)[C_{2}]$	\(q+(\beta _{1}+\beta _{4})q^{7}+\beta _{2}q^{11}+(-5\beta _{1}-2\beta _{4}+\cdots)q^{13}+\cdots\)
1800.3.c.d	$1800$	$3$	1800.c	15.d	$2$	$8$	$8$	$49.046$	8.0.40960000.1	None					360.3.l.b	$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2^{11}$	$\mathrm{SU}(2)[C_{2}]$	\(q-\beta _{5}q^{7}+(\beta _{2}-\beta _{4})q^{11}+(\beta _{1}+\beta _{5}+\cdots)q^{13}+\cdots\)
1800.3.c.e	$1800$	$3$	1800.c	15.d	$2$	$8$	$8$	$49.046$	8.0.40960000.1	None		✓			1800.3.l.b	$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2^{12}$	$\mathrm{SU}(2)[C_{2}]$	\(q+(3\beta _{1}-\beta _{6})q^{7}+(-\beta _{2}-2\beta _{5})q^{11}+\cdots\)

Decomposition of \(S_{3}^{\mathrm{old}}(1800, [\chi])\) into lower level spaces

\( S_{3}^{\mathrm{old}}(1800, [\chi]) \simeq \) \(S_{3}^{\mathrm{new}}(15, [\chi])\)\(^{\oplus 16}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(30, [\chi])\)\(^{\oplus 12}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(45, [\chi])\)\(^{\oplus 8}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(60, [\chi])\)\(^{\oplus 8}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(75, [\chi])\)\(^{\oplus 8}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(90, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(120, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(150, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(180, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(225, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(300, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(360, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(450, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(600, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(900, [\chi])\)\(^{\oplus 2}\)