Space of modular forms of level 105, weight 4, and Character 105.d

• Label: 105.4.d
• Level: $105$
• Weight: $4$
• Character orbit: 105.d
• Rep. character: $\chi_{105}(64,\cdot)$
• Character field: $\Q$
• Dimension: $16$
• Newform subspaces: $2$
• Sturm bound: $64$
• Trace bound: $1$

Defining parameters

Level:	\( N \)	\(=\)	\( 105 = 3 \cdot 5 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	105.d (of order \(2\) and degree \(1\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 5 \)
Character field:			\(\Q\)
Newform subspaces:			\( 2 \)
Sturm bound:			\(64\)
Trace bound:			\(1\)
Distinguishing \(T_p\):			\(2\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{4}(105, [\chi])\).

	Total	New	Old
Modular forms	52	16	36
Cusp forms	44	16	28
Eisenstein series	8	0	8

Trace form

16 * q - 60 * q^4 - 28 * q^5 - 12 * q^6 - 144 * q^9 + 8 * q^10 - 24 * q^15 + 172 * q^16 - 72 * q^19 + 700 * q^20 - 84 * q^21 + 324 * q^24 - 8 * q^25 + 696 * q^26 - 1080 * q^29 - 432 * q^30 - 48 * q^31 - 152 * q^34 + 56 * q^35 + 540 * q^36 + 600 * q^39 - 2144 * q^40 + 1192 * q^41 + 32 * q^44 + 252 * q^45 - 64 * q^46 - 784 * q^49 - 1288 * q^50 - 1560 * q^51 + 108 * q^54 + 1408 * q^55 + 168 * q^56 + 352 * q^59 - 228 * q^60 - 440 * q^61 + 1476 * q^64 - 3312 * q^65 + 1920 * q^66 - 1776 * q^69 - 756 * q^70 + 904 * q^71 + 664 * q^74 + 528 * q^75 + 7840 * q^76 + 4880 * q^79 - 332 * q^80 + 1296 * q^81 + 1008 * q^84 - 1272 * q^85 - 4200 * q^86 + 3304 * q^89 - 72 * q^90 - 1456 * q^91 - 9304 * q^94 + 440 * q^95 + 1236 * q^96

Decomposition of \(S_{4}^{\mathrm{new}}(105, [\chi])\) 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
																		$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
105.4.d.a	$105$	$4$	105.d	5.b	$2$	$6$	$6$	$6.195$	6.0.84052224.1	None		✓			105.4.d.a	$2$	$0$	\(0\)	\(0\)	\(-14\)	\(0\)	$2^{2}$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta _{1}q^{2}-3\beta _{3}q^{3}+(-1-2\beta _{2}-\beta _{4}+\cdots)q^{4}+\cdots\)
105.4.d.b	$105$	$4$	105.d	5.b	$2$	$10$	$10$	$6.195$	\(\mathbb{Q}[x]/(x^{10} + \cdots)\)	None		✓	✓		105.4.d.b	$2$	$0$	\(0\)	\(0\)	\(-14\)	\(0\)	$2^{9}\cdot 5$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta _{6}q^{2}-3\beta _{2}q^{3}+(-5-\beta _{1}+\beta _{5}+\cdots)q^{4}+\cdots\)

Decomposition of \(S_{4}^{\mathrm{old}}(105, [\chi])\) into lower level spaces

\( S_{4}^{\mathrm{old}}(105, [\chi]) \simeq \) \(S_{4}^{\mathrm{new}}(15, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(35, [\chi])\)\(^{\oplus 2}\)