Space of modular forms of level 275, weight 2, and Character 275.e

• Label: 275.2.e
• Level: $275$
• Weight: $2$
• Character orbit: 275.e
• Rep. character: $\chi_{275}(32,\cdot)$
• Character field: $\Q(\zeta_{4})$
• Dimension: $32$
• Newform subspaces: $4$
• Sturm bound: $60$
• Trace bound: $3$

Defining parameters

Level:	$N$	$=$	$275 = 5^{2} \cdot 11$
Weight:	$k$	$=$	$2$
Character orbit:	$[\chi]$	$=$	275.e (of order $4$ and degree $2$)
Character conductor:	$\operatorname{cond}(\chi)$	$=$	$55$
Character field:			$\Q(i)$
Newform subspaces:			$4$
Sturm bound:			$60$
Trace bound:			$3$
Distinguishing $T_p$:			$2$

Dimensions

The following table gives the dimensions of various subspaces of $M_{2}(275, [\chi])$.

	Total	New	Old
Modular forms	72	40	32
Cusp forms	48	32	16
Eisenstein series	24	8	16

Trace form

32 * q + 6 * q^3 - 20 * q^11 - 8 * q^12 - 12 * q^16 + 20 * q^22 - 14 * q^23 + 56 * q^26 - 6 * q^27 - 40 * q^31 + 26 * q^33 + 12 * q^36 + 2 * q^37 - 40 * q^38 + 12 * q^47 - 4 * q^48 + 16 * q^53 - 48 * q^56 + 40 * q^58 - 80 * q^66 - 38 * q^67 + 4 * q^71 - 40 * q^78 - 60 * q^81 - 40 * q^82 - 24 * q^86 + 20 * q^88 - 24 * q^91 - 48 * q^92 - 58 * q^93 + 62 * q^97

Decomposition of $S_{2}^{\mathrm{new}}(275, [\chi])$ 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
																		$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
275.2.e.a	$275$	$2$	275.e	55.e	$4$	$4$	$2$	$2.196$	$\Q(i, \sqrt{11})$	$\Q(\sqrt{-11})$					55.2.e.b	$4$	$0$	$0$	$2$	$0$	$0$	$2$	$\mathrm{U}(1)[D_{4}]$	$q+(\beta _{1}-\beta _{2})q^{3}-2\beta _{1}q^{4}+(-1+3\beta _{1}+\cdots)q^{9}+\cdots$
275.2.e.b	$275$	$2$	275.e	55.e	$4$	$4$	$2$	$2.196$	$\Q(i, \sqrt{10})$	None					55.2.e.a	$4$	$0$	$0$	$4$	$0$	$0$	$1$	$\mathrm{SU}(2)[C_{4}]$	$q+\beta _{1}q^{2}+(1+\beta _{2})q^{3}+3\beta _{2}q^{4}+(\beta _{1}+\cdots)q^{6}+\cdots$
275.2.e.c	$275$	$2$	275.e	55.e	$4$	$8$	$4$	$2.196$	8.0.1499238400.2	$\Q(\sqrt{-55})$		✓			275.2.e.c	$8$	$0$	$0$	$0$	$0$	$0$	$2^{6}$	$\mathrm{U}(1)[D_{4}]$	$q-\beta _{2}q^{2}+(-2\beta _{4}-\beta _{6})q^{4}+\beta _{5}q^{7}+\cdots$
275.2.e.d	$275$	$2$	275.e	55.e	$4$	$16$	$8$	$2.196$	16.0.$\cdots$.2	None		✓	✓		275.2.e.d	$8$	$0$	$0$	$0$	$0$	$0$	$2^{8}$	$\mathrm{SU}(2)[C_{4}]$	$q+\beta _{9}q^{2}+(-\beta _{3}-\beta _{10})q^{3}+(\beta _{4}-\beta _{7}+\cdots)q^{4}+\cdots$

Decomposition of $S_{2}^{\mathrm{old}}(275, [\chi])$ into lower level spaces

$S_{2}^{\mathrm{old}}(275, [\chi]) \simeq$ $S_{2}^{\mathrm{new}}(55, [\chi])$$^{\oplus 2}$