Space of modular forms of level 2025, weight 2, and Character 2025.b

• Label: 2025.2.b
• Level: $2025$
• Weight: $2$
• Character orbit: 2025.b
• Rep. character: $\chi_{2025}(649,\cdot)$
• Character field: $\Q$
• Dimension: $68$
• Newform subspaces: $16$
• Sturm bound: $540$
• Trace bound: $11$

Defining parameters

Level:	\( N \)	\(=\)	\( 2025 = 3^{4} \cdot 5^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	2025.b (of order \(2\) and degree \(1\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 5 \)
Character field:			\(\Q\)
Newform subspaces:			\( 16 \)
Sturm bound:			\(540\)
Trace bound:			\(11\)
Distinguishing \(T_p\):			\(2\), \(11\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(2025, [\chi])\).

	Total	New	Old
Modular forms	306	76	230
Cusp forms	234	68	166
Eisenstein series	72	8	64

Trace form

\( 68 q - 68 q^{4} + 68 q^{16} + 8 q^{19} + 16 q^{31} + 24 q^{34} - 48 q^{46} - 56 q^{61} - 32 q^{64} - 92 q^{76} - 4 q^{79} + 44 q^{91} - 60 q^{94}+O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(2025, [\chi])\) 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
																		$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
2025.2.b.a	$2025$	$2$	2025.b	5.b	$2$	$2$	$2$	$16.170$	\(\Q(\sqrt{-1}) \)	None					405.2.a.a	$2$	$1$	\(0\)	\(0\)	\(0\)	\(0\)	$2$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta q^{2}-2 q^{4}-5 q^{11}+2\beta q^{13}+\cdots\)
2025.2.b.b	$2025$	$2$	2025.b	5.b	$2$	$2$	$2$	$16.170$	\(\Q(\sqrt{-1}) \)	None					405.2.a.a	$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta q^{2}-2 q^{4}+5 q^{11}-2\beta q^{13}+\cdots\)
2025.2.b.c	$2025$	$2$	2025.b	5.b	$2$	$2$	$2$	$16.170$	\(\Q(\sqrt{-1}) \)	None					45.2.e.a	$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+i q^{2}+q^{4}-3 i q^{7}+3 i q^{8}-2 q^{11}+\cdots\)
2025.2.b.d	$2025$	$2$	2025.b	5.b	$2$	$2$	$2$	$16.170$	\(\Q(\sqrt{-1}) \)	None					45.2.e.a	$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+i q^{2}+q^{4}+3 i q^{7}+3 i q^{8}+2 q^{11}+\cdots\)
2025.2.b.e	$2025$	$2$	2025.b	5.b	$2$	$2$	$2$	$16.170$	\(\Q(\sqrt{-1}) \)	None					405.2.a.c	$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2$	$\mathrm{SU}(2)[C_{2}]$	\(q+2 q^{4}-\beta q^{7}-3 q^{11}-2\beta q^{13}+\cdots\)
2025.2.b.f	$2025$	$2$	2025.b	5.b	$2$	$2$	$2$	$16.170$	\(\Q(\sqrt{-1}) \)	None					405.2.a.c	$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2$	$\mathrm{SU}(2)[C_{2}]$	\(q+2 q^{4}-\beta q^{7}+3 q^{11}-2\beta q^{13}+\cdots\)
2025.2.b.g	$2025$	$2$	2025.b	5.b	$2$	$4$	$4$	$16.170$	\(\Q(\zeta_{12})\)	None					405.2.a.g	$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2^{3}$	$\mathrm{SU}(2)[C_{2}]$	\(q-\beta_{3} q^{2}+(2\beta_1-2)q^{4}+(\beta_{3}+2\beta_{2})q^{7}+\cdots\)
2025.2.b.h	$2025$	$2$	2025.b	5.b	$2$	$4$	$4$	$16.170$	\(\Q(\zeta_{12})\)	None					405.2.a.g	$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2^{3}$	$\mathrm{SU}(2)[C_{2}]$	\(q-\beta_{3} q^{2}+(2\beta_1-2)q^{4}+(-\beta_{3}-2\beta_{2})q^{7}+\cdots\)
2025.2.b.i	$2025$	$2$	2025.b	5.b	$2$	$4$	$4$	$16.170$	\(\Q(i, \sqrt{13})\)	None		✓			2025.2.a.h	$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta _{1}q^{2}+(-2+\beta _{3})q^{4}+(-\beta _{1}+2\beta _{2}+\cdots)q^{7}+\cdots\)
2025.2.b.j	$2025$	$2$	2025.b	5.b	$2$	$4$	$4$	$16.170$	\(\Q(i, \sqrt{13})\)	None		✓			2025.2.a.h	$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta _{1}q^{2}+(-2+\beta _{3})q^{4}+(\beta _{1}-2\beta _{2}+\cdots)q^{7}+\cdots\)
2025.2.b.k	$2025$	$2$	2025.b	5.b	$2$	$4$	$4$	$16.170$	\(\Q(\zeta_{12})\)	None					81.2.a.a	$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2^{2}$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta_{2} q^{2}-q^{4}-2\beta_1 q^{7}+\beta_{2} q^{8}+\cdots\)
2025.2.b.l	$2025$	$2$	2025.b	5.b	$2$	$6$	$6$	$16.170$	6.0.5089536.1	None					45.2.e.b	$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2^{3}$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta _{5}q^{2}+(-2+\beta _{3})q^{4}+(-\beta _{4}-\beta _{5})q^{7}+\cdots\)
2025.2.b.m	$2025$	$2$	2025.b	5.b	$2$	$6$	$6$	$16.170$	6.0.5089536.1	None					45.2.e.b	$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2^{3}$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta _{5}q^{2}+(-2+\beta _{3})q^{4}+(\beta _{4}+\beta _{5})q^{7}+\cdots\)
2025.2.b.n	$2025$	$2$	2025.b	5.b	$2$	$8$	$8$	$16.170$	8.0.\(\cdots\).6	None					225.2.e.c	$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta _{1}q^{2}+(-1+\beta _{4}-\beta _{6})q^{4}+(-\beta _{2}+\cdots)q^{7}+\cdots\)
2025.2.b.o	$2025$	$2$	2025.b	5.b	$2$	$8$	$8$	$16.170$	8.0.\(\cdots\).6	None					225.2.e.c	$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta _{1}q^{2}+(-1+\beta _{4}-\beta _{6})q^{4}+(\beta _{2}+\cdots)q^{7}+\cdots\)
2025.2.b.p	$2025$	$2$	2025.b	5.b	$2$	$8$	$8$	$16.170$	8.0.49787136.1	None		✓			2025.2.a.u	$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2^{4}$	$\mathrm{SU}(2)[C_{2}]$	\(q-\beta _{6}q^{2}+\beta _{4}q^{4}+(-\beta _{1}+2\beta _{3})q^{7}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(2025, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(2025, [\chi]) \simeq \) \(S_{2}^{\mathrm{new}}(45, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(75, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(135, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(225, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(405, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(675, [\chi])\)\(^{\oplus 2}\)