Space of modular forms of level 2300, weight 2, and Character 2300.i

• Label: 2300.2.i
• Level: $2300$
• Weight: $2$
• Character orbit: 2300.i
• Rep. character: $\chi_{2300}(1057,\cdot)$
• Character field: $\Q(\zeta_{4})$
• Dimension: $72$
• Newform subspaces: $6$
• Sturm bound: $720$
• Trace bound: $31$

Defining parameters

Level:	\( N \)	\(=\)	\( 2300 = 2^{2} \cdot 5^{2} \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	2300.i (of order \(4\) and degree \(2\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 115 \)
Character field:			\(\Q(i)\)
Newform subspaces:			\( 6 \)
Sturm bound:			\(720\)
Trace bound:			\(31\)
Distinguishing \(T_p\):			\(3\), \(19\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(2300, [\chi])\).

	Total	New	Old
Modular forms	756	72	684
Cusp forms	684	72	612
Eisenstein series	72	0	72

Trace form

\( 72 q + 4 q^{3} + O(q^{10}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(2300, [\chi])\) 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
														$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
2300.2.i.a	$2300$	$2$	2300.i	115.e	$4$	$8$	$4$	$18.366$	8.0.\(\cdots\).122	\(\Q(\sqrt{-115}) \)		$8$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$	$\mathrm{U}(1)[D_{4}]$	\(q-\beta _{1}q^{7}-3\beta _{2}q^{9}+(\beta _{1}-2\beta _{5})q^{17}+\cdots\)
2300.2.i.b	$2300$	$2$	2300.i	115.e	$4$	$8$	$4$	$18.366$	8.0.157351936.1	None		$8$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2^{8}$	$\mathrm{SU}(2)[C_{4}]$	\(q+\beta _{2}q^{3}-\beta _{5}q^{7}+4\beta _{3}q^{9}-\beta _{1}q^{11}+\cdots\)
2300.2.i.c	$2300$	$2$	2300.i	115.e	$4$	$8$	$4$	$18.366$	8.0.\(\cdots\).3	None		$4$	$0$	\(0\)	\(8\)	\(0\)	\(0\)	$2$	$\mathrm{SU}(2)[C_{4}]$	\(q+(1+\beta _{3})q^{3}+\beta _{2}q^{7}-\beta _{3}q^{9}+(\beta _{1}+\cdots)q^{11}+\cdots\)
2300.2.i.d	$2300$	$2$	2300.i	115.e	$4$	$16$	$8$	$18.366$	\(\mathbb{Q}[x]/(x^{16} - \cdots)\)	None		$4$	$0$	\(0\)	\(-4\)	\(0\)	\(0\)	$2^{4}$	$\mathrm{SU}(2)[C_{4}]$	\(q+\beta _{5}q^{3}+(\beta _{10}-\beta _{12}-\beta _{15})q^{7}+(\beta _{3}+\cdots)q^{9}+\cdots\)
2300.2.i.e	$2300$	$2$	2300.i	115.e	$4$	$16$	$8$	$18.366$	\(\mathbb{Q}[x]/(x^{16} + \cdots)\)	None		$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{4}]$	\(q+\beta _{1}q^{3}+(\beta _{1}+\beta _{5}-\beta _{9})q^{7}+(\beta _{6}-\beta _{7}+\cdots)q^{9}+\cdots\)
2300.2.i.f	$2300$	$2$	2300.i	115.e	$4$	$16$	$8$	$18.366$	\(\mathbb{Q}[x]/(x^{16} + \cdots)\)	None		$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{4}]$	\(q+\beta _{1}q^{3}+(-\beta _{1}-\beta _{5}+\beta _{9})q^{7}+(\beta _{6}+\cdots)q^{9}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(2300, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(2300, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(115, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(230, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(460, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(575, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(1150, [\chi])\)\(^{\oplus 2}\)