Space of modular forms of level 405, weight 2, and Character 405.m

• Label: 405.2.m
• Level: $405$
• Weight: $2$
• Character orbit: 405.m
• Rep. character: $\chi_{405}(53,\cdot)$
• Character field: $\Q(\zeta_{12})$
• Dimension: $88$
• Newform subspaces: $5$
• Sturm bound: $108$
• Trace bound: $7$

Defining parameters

Level:	\( N \)	\(=\)	\( 405 = 3^{4} \cdot 5 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	405.m (of order \(12\) and degree \(4\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 45 \)
Character field:			\(\Q(\zeta_{12})\)
Newform subspaces:			\( 5 \)
Sturm bound:			\(108\)
Trace bound:			\(7\)
Distinguishing \(T_p\):			\(2\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(405, [\chi])\).

	Total	New	Old
Modular forms	264	104	160
Cusp forms	168	88	80
Eisenstein series	96	16	80

Trace form

88 * q + 4 * q^7 - 8 * q^10 + 4 * q^13 + 40 * q^16 - 4 * q^22 - 8 * q^25 + 8 * q^28 + 8 * q^31 - 32 * q^37 - 12 * q^40 + 4 * q^43 - 184 * q^46 - 20 * q^52 + 8 * q^55 + 72 * q^58 - 16 * q^61 - 8 * q^67 + 24 * q^70 - 8 * q^73 - 84 * q^76 - 16 * q^82 - 8 * q^85 - 156 * q^88 + 32 * q^91 - 20 * q^97

Decomposition of \(S_{2}^{\mathrm{new}}(405, [\chi])\) 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
																		$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
405.2.m.a	$405$	$2$	405.m	45.l	$12$	$8$	$2$	$3.234$	\(\Q(\zeta_{24})\)	None					45.2.f.a	$8$	$0$	\(0\)	\(0\)	\(0\)	\(8\)	$1$	$\mathrm{SU}(2)[C_{12}]$	\(q+\zeta_{24}^{7}q^{2}+\zeta_{24}^{2}q^{4}+(-\zeta_{24}^{3}+2\zeta_{24}^{5}+\cdots)q^{5}+\cdots\)
405.2.m.b	$405$	$2$	405.m	45.l	$12$	$16$	$4$	$3.234$	16.0.\(\cdots\).2	None					135.2.f.b	$8$	$0$	\(0\)	\(0\)	\(0\)	\(-8\)	$3^{4}$	$\mathrm{SU}(2)[C_{12}]$	\(q+(\beta _{9}-\beta _{10})q^{2}+(-2\beta _{1}-\beta _{13}-\beta _{14}+\cdots)q^{4}+\cdots\)
405.2.m.c	$405$	$2$	405.m	45.l	$12$	$16$	$4$	$3.234$	16.0.\(\cdots\).1	None					135.2.f.a	$8$	$0$	\(0\)	\(0\)	\(0\)	\(4\)	$3^{4}$	$\mathrm{SU}(2)[C_{12}]$	\(q-\beta _{10}q^{2}+(-\beta _{9}-\beta _{15})q^{4}+(-\beta _{7}+\cdots)q^{5}+\cdots\)
405.2.m.d	$405$	$2$	405.m	45.l	$12$	$24$	$6$	$3.234$		None		✓			405.2.f.b	$4$	$0$	\(0\)	\(0\)	\(0\)	\(-12\)		$\mathrm{SU}(2)[C_{12}]$
405.2.m.e	$405$	$2$	405.m	45.l	$12$	$24$	$6$	$3.234$		None		✓			405.2.f.b	$4$	$0$	\(0\)	\(0\)	\(0\)	\(12\)		$\mathrm{SU}(2)[C_{12}]$

Decomposition of \(S_{2}^{\mathrm{old}}(405, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(405, [\chi]) \simeq \) \(S_{2}^{\mathrm{new}}(45, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(135, [\chi])\)\(^{\oplus 2}\)