Space of modular forms of level 2175, weight 2, and Character 2175.c

• Label: 2175.2.c
• Level: $2175$
• Weight: $2$
• Character orbit: 2175.c
• Rep. character: $\chi_{2175}(349,\cdot)$
• Character field: $\Q$
• Dimension: $84$
• Newform subspaces: $16$
• Sturm bound: $600$
• Trace bound: $11$

Defining parameters

Level:	\( N \)	\(=\)	\( 2175 = 3 \cdot 5^{2} \cdot 29 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	2175.c (of order \(2\) and degree \(1\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 5 \)
Character field:			\(\Q\)
Newform subspaces:			\( 16 \)
Sturm bound:			\(600\)
Trace bound:			\(11\)
Distinguishing \(T_p\):			\(2\), \(7\), \(11\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(2175, [\chi])\).

	Total	New	Old
Modular forms	312	84	228
Cusp forms	288	84	204
Eisenstein series	24	0	24

Trace form

84 * q - 92 * q^4 + 8 * q^6 - 84 * q^9 + 8 * q^11 - 24 * q^14 + 124 * q^16 - 12 * q^19 - 12 * q^21 - 24 * q^24 + 8 * q^26 - 12 * q^31 - 48 * q^34 + 92 * q^36 + 20 * q^39 + 48 * q^41 - 48 * q^44 - 40 * q^46 - 136 * q^49 + 32 * q^51 - 8 * q^54 + 96 * q^56 - 72 * q^59 + 28 * q^61 - 148 * q^64 - 32 * q^66 - 32 * q^69 + 48 * q^71 + 40 * q^74 - 24 * q^76 - 24 * q^79 + 84 * q^81 + 40 * q^84 + 8 * q^86 - 72 * q^89 + 60 * q^91 + 24 * q^94 - 24 * q^96 - 8 * q^99

Decomposition of \(S_{2}^{\mathrm{new}}(2175, [\chi])\) 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
																		$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
2175.2.c.a	$2175$	$2$	2175.c	5.b	$2$	$2$	$2$	$17.367$	\(\Q(\sqrt{-1}) \)	None					435.2.a.a	$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+i q^{2}+i q^{3}+q^{4}-q^{6}+4 i q^{7}+\cdots\)
2175.2.c.b	$2175$	$2$	2175.c	5.b	$2$	$2$	$2$	$17.367$	\(\Q(\sqrt{-1}) \)	None					435.2.a.d	$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+i q^{2}-i q^{3}+q^{4}+q^{6}+4 i q^{7}+\cdots\)
2175.2.c.c	$2175$	$2$	2175.c	5.b	$2$	$2$	$2$	$17.367$	\(\Q(\sqrt{-1}) \)	None		✓			2175.2.a.e	$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q-i q^{3}+2 q^{4}-i q^{7}-q^{9}-2 q^{11}+\cdots\)
2175.2.c.d	$2175$	$2$	2175.c	5.b	$2$	$2$	$2$	$17.367$	\(\Q(\sqrt{-1}) \)	None					435.2.a.b	$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q-i q^{3}+2 q^{4}+2 i q^{7}-q^{9}+q^{11}+\cdots\)
2175.2.c.e	$2175$	$2$	2175.c	5.b	$2$	$2$	$2$	$17.367$	\(\Q(\sqrt{-1}) \)	None					435.2.a.c	$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+i q^{3}+2 q^{4}-2 i q^{7}-q^{9}+3 q^{11}+\cdots\)
2175.2.c.f	$2175$	$2$	2175.c	5.b	$2$	$4$	$4$	$17.367$	\(\Q(i, \sqrt{21})\)	None					435.2.a.f	$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta _{1}q^{2}-\beta _{2}q^{3}+(-4+\beta _{3})q^{4}+(-1+\cdots)q^{6}+\cdots\)
2175.2.c.g	$2175$	$2$	2175.c	5.b	$2$	$4$	$4$	$17.367$	\(\Q(i, \sqrt{5})\)	None					435.2.a.g	$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2^{2}$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta _{2}q^{2}+\beta _{1}q^{3}-3q^{4}-\beta _{3}q^{6}-2\beta _{1}q^{7}+\cdots\)
2175.2.c.h	$2175$	$2$	2175.c	5.b	$2$	$4$	$4$	$17.367$	\(\Q(i, \sqrt{17})\)	None					435.2.a.h	$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta _{1}q^{2}+\beta _{2}q^{3}+(-3+\beta _{3})q^{4}+(1+\cdots)q^{6}+\cdots\)
2175.2.c.i	$2175$	$2$	2175.c	5.b	$2$	$4$	$4$	$17.367$	\(\Q(\zeta_{8})\)	None		✓			2175.2.a.n	$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta_{2} q^{2}+\beta_1 q^{3}-\beta_{3} q^{6}+\beta_1 q^{7}+\cdots\)
2175.2.c.j	$2175$	$2$	2175.c	5.b	$2$	$4$	$4$	$17.367$	\(\Q(i, \sqrt{5})\)	None					435.2.a.e	$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta _{1}q^{2}-\beta _{3}q^{3}+(1+\beta _{2})q^{4}+\beta _{2}q^{6}+\cdots\)
2175.2.c.k	$2175$	$2$	2175.c	5.b	$2$	$4$	$4$	$17.367$	\(\Q(i, \sqrt{5})\)	None					87.2.a.a	$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta _{1}q^{2}+\beta _{3}q^{3}+(1+\beta _{2})q^{4}-\beta _{2}q^{6}+\cdots\)
2175.2.c.l	$2175$	$2$	2175.c	5.b	$2$	$6$	$6$	$17.367$	6.0.3356224.1	None					87.2.a.b	$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+(\beta _{3}-\beta _{5})q^{2}+\beta _{3}q^{3}+(-2-\beta _{4}+\cdots)q^{4}+\cdots\)
2175.2.c.m	$2175$	$2$	2175.c	5.b	$2$	$6$	$6$	$17.367$	6.0.14077504.1	None					435.2.a.i	$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta _{1}q^{2}+\beta _{2}q^{3}+(-2+\beta _{3})q^{4}-\beta _{5}q^{6}+\cdots\)
2175.2.c.n	$2175$	$2$	2175.c	5.b	$2$	$8$	$8$	$17.367$	8.0.1267360000.3	None					435.2.a.j	$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2^{2}$	$\mathrm{SU}(2)[C_{2}]$	\(q+(\beta _{1}+\beta _{5})q^{2}-\beta _{5}q^{3}+(-2+\beta _{4}+\cdots)q^{4}+\cdots\)
2175.2.c.o	$2175$	$2$	2175.c	5.b	$2$	$14$	$14$	$17.367$	\(\mathbb{Q}[x]/(x^{14} + \cdots)\)	None		✓			2175.2.a.ba	$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta _{1}q^{2}-\beta _{9}q^{3}+(-1+\beta _{2})q^{4}+\beta _{6}q^{6}+\cdots\)
2175.2.c.p	$2175$	$2$	2175.c	5.b	$2$	$16$	$16$	$17.367$	\(\mathbb{Q}[x]/(x^{16} + \cdots)\)	None		✓	✓		2175.2.a.bc	$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2^{2}$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta _{1}q^{2}-\beta _{6}q^{3}+(-2+\beta _{2})q^{4}-\beta _{3}q^{6}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(2175, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(2175, [\chi]) \simeq \) \(S_{2}^{\mathrm{new}}(75, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(145, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(435, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(725, [\chi])\)\(^{\oplus 2}\)