Space of modular forms of level 104, weight 2, and Character 104.m

• Label: 104.2.m
• Level: $104$
• Weight: $2$
• Character orbit: 104.m
• Rep. character: $\chi_{104}(83,\cdot)$
• Character field: $\Q(\zeta_{4})$
• Dimension: $24$
• Newform subspaces: $2$
• Sturm bound: $28$
• Trace bound: $1$

Defining parameters

Level:	\( N \)	\(=\)	\( 104 = 2^{3} \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	104.m (of order \(4\) and degree \(2\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 104 \)
Character field:			\(\Q(i)\)
Newform subspaces:			\( 2 \)
Sturm bound:			\(28\)
Trace bound:			\(1\)
Distinguishing \(T_p\):			\(3\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(104, [\chi])\).

	Total	New	Old
Modular forms	32	32	0
Cusp forms	24	24	0
Eisenstein series	8	8	0

Trace form

24 * q - 2 * q^2 - 8 * q^3 + 4 * q^8 + 8 * q^9 - 4 * q^11 - 20 * q^14 + 4 * q^16 - 18 * q^18 - 4 * q^19 + 8 * q^20 - 16 * q^22 - 4 * q^24 - 34 * q^26 - 32 * q^27 + 12 * q^28 + 8 * q^32 - 16 * q^33 + 16 * q^34 - 8 * q^35 + 44 * q^40 + 28 * q^42 + 40 * q^44 + 20 * q^46 - 4 * q^48 - 26 * q^50 + 36 * q^52 + 4 * q^54 + 12 * q^58 + 52 * q^59 - 56 * q^60 - 8 * q^65 + 64 * q^66 - 4 * q^67 - 52 * q^68 + 60 * q^70 - 60 * q^72 + 40 * q^74 + 28 * q^76 + 68 * q^78 - 12 * q^80 - 40 * q^81 + 36 * q^83 - 60 * q^84 - 32 * q^86 - 24 * q^89 - 20 * q^91 - 88 * q^92 - 44 * q^94 - 100 * q^96 - 16 * q^97 - 2 * q^98 + 12 * q^99

Decomposition of \(S_{2}^{\mathrm{new}}(104, [\chi])\) 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
																		$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
104.2.m.a	$104$	$2$	104.m	104.m	$4$	$4$	$2$	$0.830$	\(\Q(i, \sqrt{26})\)	None		✓			104.2.m.a	$4$	$0$	\(-4\)	\(-4\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{4}]$	\(q+(-1-\beta _{2})q^{2}-q^{3}+2\beta _{2}q^{4}-\beta _{3}q^{5}+\cdots\)
104.2.m.b	$104$	$2$	104.m	104.m	$4$	$20$	$10$	$0.830$	\(\mathbb{Q}[x]/(x^{20} - \cdots)\)	None		✓	✓		104.2.m.b	$4$	$0$	\(2\)	\(-4\)	\(0\)	\(0\)	$2^{6}$	$\mathrm{SU}(2)[C_{4}]$	\(q-\beta _{14}q^{2}-\beta _{5}q^{3}-\beta _{2}q^{4}+\beta _{10}q^{5}+\cdots\)