Space of modular forms of level 825, weight 2, and Character 825.n

• Label: 825.2.n
• Level: $825$
• Weight: $2$
• Character orbit: 825.n
• Rep. character: $\chi_{825}(301,\cdot)$
• Character field: $\Q(\zeta_{5})$
• Dimension: $152$
• Newform subspaces: $16$
• Sturm bound: $240$
• Trace bound: $11$

Defining parameters

Level:	\( N \)	\(=\)	\( 825 = 3 \cdot 5^{2} \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	825.n (of order \(5\) and degree \(4\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 11 \)
Character field:			\(\Q(\zeta_{5})\)
Newform subspaces:			\( 16 \)
Sturm bound:			\(240\)
Trace bound:			\(11\)
Distinguishing \(T_p\):			\(2\), \(13\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(825, [\chi])\).

	Total	New	Old
Modular forms	528	152	376
Cusp forms	432	152	280
Eisenstein series	96	0	96

Trace form

152 * q - 4 * q^2 - 42 * q^4 + 2 * q^6 - 6 * q^7 + 8 * q^8 - 38 * q^9 + 10 * q^11 + 8 * q^12 + 6 * q^13 - 6 * q^14 - 34 * q^16 + 2 * q^17 + 6 * q^18 + 20 * q^19 - 16 * q^21 + 36 * q^22 + 20 * q^23 + 24 * q^24 - 18 * q^26 - 16 * q^28 - 4 * q^29 - 8 * q^32 + 6 * q^33 - 40 * q^34 - 42 * q^36 + 46 * q^37 + 46 * q^38 + 16 * q^39 - 28 * q^41 - 22 * q^42 + 24 * q^43 + 70 * q^44 + 70 * q^46 + 18 * q^47 - 40 * q^48 - 76 * q^49 - 8 * q^51 - 62 * q^52 - 26 * q^53 - 8 * q^54 - 156 * q^56 - 8 * q^57 + 44 * q^58 - 14 * q^59 - 14 * q^61 + 12 * q^62 - 6 * q^63 - 118 * q^64 - 12 * q^66 + 12 * q^67 + 68 * q^68 - 2 * q^69 + 4 * q^71 - 2 * q^72 + 16 * q^73 + 50 * q^74 + 48 * q^76 + 94 * q^77 - 80 * q^78 + 34 * q^79 - 38 * q^81 + 50 * q^82 - 30 * q^83 + 72 * q^84 + 64 * q^87 + 42 * q^88 + 76 * q^89 + 26 * q^91 + 70 * q^92 - 52 * q^93 + 54 * q^94 + 20 * q^96 - 30 * q^97 - 136 * q^98 + 20 * q^99

Decomposition of \(S_{2}^{\mathrm{new}}(825, [\chi])\) 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
																		$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
825.2.n.a	$825$	$2$	825.n	11.c	$5$	$4$	$1$	$6.588$	\(\Q(\zeta_{10})\)	None		✓			825.2.n.a	$2$	$0$	\(-3\)	\(-1\)	\(0\)	\(-3\)	$1$	$\mathrm{SU}(2)[C_{5}]$	\(q+(-1+\zeta_{10}^{3})q^{2}+\zeta_{10}^{2}q^{3}+(1-\zeta_{10}+\cdots)q^{4}+\cdots\)
825.2.n.b	$825$	$2$	825.n	11.c	$5$	$4$	$1$	$6.588$	\(\Q(\zeta_{10})\)	None		✓			825.2.n.b	$2$	$0$	\(-2\)	\(1\)	\(0\)	\(8\)	$1$	$\mathrm{SU}(2)[C_{5}]$	\(q+(-\zeta_{10}+\zeta_{10}^{2})q^{2}-\zeta_{10}^{2}q^{3}+(-1+\cdots)q^{4}+\cdots\)
825.2.n.c	$825$	$2$	825.n	11.c	$5$	$4$	$1$	$6.588$	\(\Q(\zeta_{10})\)	None					33.2.e.b	$2$	$1$	\(1\)	\(-1\)	\(0\)	\(-1\)	$1$	$\mathrm{SU}(2)[C_{5}]$	\(q+(-1+2\zeta_{10}-2\zeta_{10}^{2}+\zeta_{10}^{3})q^{2}+\cdots\)
825.2.n.d	$825$	$2$	825.n	11.c	$5$	$4$	$1$	$6.588$	\(\Q(\zeta_{10})\)	None		✓			825.2.n.b	$2$	$0$	\(2\)	\(-1\)	\(0\)	\(-8\)	$1$	$\mathrm{SU}(2)[C_{5}]$	\(q+(\zeta_{10}-\zeta_{10}^{2})q^{2}+\zeta_{10}^{2}q^{3}+(-1+\cdots)q^{4}+\cdots\)
825.2.n.e	$825$	$2$	825.n	11.c	$5$	$4$	$1$	$6.588$	\(\Q(\zeta_{10})\)	None		✓			825.2.n.a	$2$	$0$	\(3\)	\(1\)	\(0\)	\(3\)	$1$	$\mathrm{SU}(2)[C_{5}]$	\(q+(1-\zeta_{10}^{3})q^{2}-\zeta_{10}^{2}q^{3}+(1-\zeta_{10}+\cdots)q^{4}+\cdots\)
825.2.n.f	$825$	$2$	825.n	11.c	$5$	$4$	$1$	$6.588$	\(\Q(\zeta_{10})\)	None					33.2.e.a	$2$	$0$	\(3\)	\(1\)	\(0\)	\(3\)	$1$	$\mathrm{SU}(2)[C_{5}]$	\(q+(1-\zeta_{10}^{3})q^{2}-\zeta_{10}^{2}q^{3}+(1-\zeta_{10}+\cdots)q^{4}+\cdots\)
825.2.n.g	$825$	$2$	825.n	11.c	$5$	$8$	$2$	$6.588$	8.0.13140625.1	None					165.2.m.d	$2$	$0$	\(-4\)	\(2\)	\(0\)	\(-3\)	$1$	$\mathrm{SU}(2)[C_{5}]$	\(q+(-1-\beta _{1}-\beta _{2}+\beta _{3}-\beta _{4}+\beta _{5}+\cdots)q^{2}+\cdots\)
825.2.n.h	$825$	$2$	825.n	11.c	$5$	$8$	$2$	$6.588$	8.0.819390625.1	None		✓			825.2.n.h	$2$	$0$	\(-3\)	\(2\)	\(0\)	\(-7\)	$1$	$\mathrm{SU}(2)[C_{5}]$	\(q-\beta _{1}q^{2}+(1+\beta _{2}+\beta _{3}-\beta _{6})q^{3}+(-1+\cdots)q^{4}+\cdots\)
825.2.n.i	$825$	$2$	825.n	11.c	$5$	$8$	$2$	$6.588$	8.0.819390625.1	None					165.2.m.b	$2$	$0$	\(-2\)	\(-2\)	\(0\)	\(-9\)	$1$	$\mathrm{SU}(2)[C_{5}]$	\(q-\beta _{4}q^{2}-\beta _{6}q^{3}+(1-\beta _{1}+2\beta _{2}+\beta _{3}+\cdots)q^{4}+\cdots\)
825.2.n.j	$825$	$2$	825.n	11.c	$5$	$8$	$2$	$6.588$	\(\Q(\zeta_{15})\)	None					165.2.m.c	$2$	$0$	\(-2\)	\(-2\)	\(0\)	\(5\)	$1$	$\mathrm{SU}(2)[C_{5}]$	\(q+(1-2\zeta_{15}+\zeta_{15}^{3}-\zeta_{15}^{4}+\zeta_{15}^{5}+\cdots)q^{2}+\cdots\)
825.2.n.k	$825$	$2$	825.n	11.c	$5$	$8$	$2$	$6.588$	8.0.13140625.1	None					165.2.m.a	$2$	$0$	\(0\)	\(2\)	\(0\)	\(-1\)	$1$	$\mathrm{SU}(2)[C_{5}]$	\(q+(-1+\beta _{3}-\beta _{4}+\beta _{5}+\beta _{6})q^{2}+(1+\cdots)q^{3}+\cdots\)
825.2.n.l	$825$	$2$	825.n	11.c	$5$	$8$	$2$	$6.588$	8.0.819390625.1	None		✓			825.2.n.h	$2$	$0$	\(3\)	\(-2\)	\(0\)	\(7\)	$1$	$\mathrm{SU}(2)[C_{5}]$	\(q+\beta _{1}q^{2}+(-1-\beta _{2}-\beta _{3}+\beta _{6})q^{3}+\cdots\)
825.2.n.m	$825$	$2$	825.n	11.c	$5$	$16$	$4$	$6.588$	\(\mathbb{Q}[x]/(x^{16} - \cdots)\)	None		✓			825.2.n.m	$2$	$0$	\(-2\)	\(-4\)	\(0\)	\(4\)	$1$	$\mathrm{SU}(2)[C_{5}]$	\(q+(-\beta _{1}+\beta _{2}-\beta _{4}-\beta _{6})q^{2}-\beta _{11}q^{3}+\cdots\)
825.2.n.n	$825$	$2$	825.n	11.c	$5$	$16$	$4$	$6.588$	\(\mathbb{Q}[x]/(x^{16} - \cdots)\)	None		✓			825.2.n.m	$2$	$0$	\(2\)	\(4\)	\(0\)	\(-4\)	$1$	$\mathrm{SU}(2)[C_{5}]$	\(q+(\beta _{1}-\beta _{2}+\beta _{4}+\beta _{6})q^{2}+\beta _{11}q^{3}+\cdots\)
825.2.n.o	$825$	$2$	825.n	11.c	$5$	$24$	$6$	$6.588$		None					165.2.s.a	$2$	$0$	\(-2\)	\(6\)	\(0\)	\(-4\)		$\mathrm{SU}(2)[C_{5}]$
825.2.n.p	$825$	$2$	825.n	11.c	$5$	$24$	$6$	$6.588$		None					165.2.s.a	$2$	$0$	\(2\)	\(-6\)	\(0\)	\(4\)		$\mathrm{SU}(2)[C_{5}]$

Decomposition of \(S_{2}^{\mathrm{old}}(825, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(825, [\chi]) \simeq \) \(S_{2}^{\mathrm{new}}(33, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(55, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(165, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(275, [\chi])\)\(^{\oplus 2}\)