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

• Label: 2300.2.c
• Level: $2300$
• Weight: $2$
• Character orbit: 2300.c
• Rep. character: $\chi_{2300}(1749,\cdot)$
• Character field: $\Q$
• Dimension: $32$
• Newform subspaces: $10$
• Sturm bound: $720$
• Trace bound: $11$

Defining parameters

Level:	\( N \)	\(=\)	\( 2300 = 2^{2} \cdot 5^{2} \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	2300.c (of order \(2\) and degree \(1\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 5 \)
Character field:			\(\Q\)
Newform subspaces:			\( 10 \)
Sturm bound:			\(720\)
Trace bound:			\(11\)
Distinguishing \(T_p\):			\(3\), \(7\), \(11\)

Dimensions

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

	Total	New	Old
Modular forms	378	32	346
Cusp forms	342	32	310
Eisenstein series	36	0	36

Trace form

\( 32 q - 20 q^{9} - 8 q^{11} - 4 q^{19} + 8 q^{21} + 36 q^{29} - 8 q^{31} - 32 q^{39} - 20 q^{41} - 16 q^{49} - 8 q^{51} + 16 q^{59} + 8 q^{69} + 48 q^{71} + 48 q^{79} - 36 q^{89} - 16 q^{91} + 28 q^{99}+O(q^{100}) \)

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	Twist minimal	Largest	Maximal	Minimal twist	Inner twists	Rank*	Traces				Coefficient ring index	Sato-Tate	$q$-expansion
																		$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
2300.2.c.a	$2300$	$2$	2300.c	5.b	$2$	$2$	$2$	$18.366$	\(\Q(\sqrt{-1}) \)	None					460.2.a.d	$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+3 i q^{3}-2 i q^{7}-6 q^{9}-3 i q^{13}+\cdots\)
2300.2.c.b	$2300$	$2$	2300.c	5.b	$2$	$2$	$2$	$18.366$	\(\Q(\sqrt{-1}) \)	None					92.2.a.a	$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+3 i q^{3}-4 i q^{7}-6 q^{9}+2 q^{11}+\cdots\)
2300.2.c.c	$2300$	$2$	2300.c	5.b	$2$	$2$	$2$	$18.366$	\(\Q(\sqrt{-1}) \)	None		✓			2300.2.a.b	$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+2 i q^{3}-i q^{7}-q^{9}-3 q^{11}-5 i q^{13}+\cdots\)
2300.2.c.d	$2300$	$2$	2300.c	5.b	$2$	$2$	$2$	$18.366$	\(\Q(\sqrt{-1}) \)	None					460.2.a.c	$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+i q^{3}+4 i q^{7}+2 q^{9}-6 q^{11}+\cdots\)
2300.2.c.e	$2300$	$2$	2300.c	5.b	$2$	$2$	$2$	$18.366$	\(\Q(\sqrt{-1}) \)	None					460.2.a.a	$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+i q^{3}-2 i q^{7}+2 q^{9}-4 q^{11}+\cdots\)
2300.2.c.f	$2300$	$2$	2300.c	5.b	$2$	$2$	$2$	$18.366$	\(\Q(\sqrt{-1}) \)	None					92.2.a.b	$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+i q^{3}-2 i q^{7}+2 q^{9}-i q^{13}+\cdots\)
2300.2.c.g	$2300$	$2$	2300.c	5.b	$2$	$2$	$2$	$18.366$	\(\Q(\sqrt{-1}) \)	None					460.2.a.b	$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+i q^{7}+3 q^{9}+6 q^{11}+6 i q^{13}+\cdots\)
2300.2.c.h	$2300$	$2$	2300.c	5.b	$2$	$4$	$4$	$18.366$	\(\Q(i, \sqrt{17})\)	None					460.2.a.e	$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta _{1}q^{3}+(\beta _{1}+\beta _{2})q^{7}+(-2+\beta _{3})q^{9}+\cdots\)
2300.2.c.i	$2300$	$2$	2300.c	5.b	$2$	$6$	$6$	$18.366$	6.0.6594624.1	None		✓			2300.2.a.j	$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+(\beta _{1}-\beta _{4})q^{3}+2\beta _{1}q^{7}+(-1+\beta _{2}+\cdots)q^{9}+\cdots\)
2300.2.c.j	$2300$	$2$	2300.c	5.b	$2$	$8$	$8$	$18.366$	8.0.\(\cdots\).1	None		✓	✓		2300.2.a.l	$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta _{1}q^{3}+(-\beta _{1}-\beta _{5})q^{7}+(-1+\beta _{2}+\cdots)q^{9}+\cdots\)

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

\( S_{2}^{\mathrm{old}}(2300, [\chi]) \simeq \) \(S_{2}^{\mathrm{new}}(50, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(100, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(115, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(230, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(460, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(575, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(1150, [\chi])\)\(^{\oplus 2}\)