Space of modular forms of level 1935, weight 2, and Character 1935.b

• Label: 1935.2.b
• Level: $1935$
• Weight: $2$
• Character orbit: 1935.b
• Rep. character: $\chi_{1935}(1549,\cdot)$
• Character field: $\Q$
• Dimension: $104$
• Newform subspaces: $7$
• Sturm bound: $528$
• Trace bound: $5$

Defining parameters

Level:	\( N \)	\(=\)	\( 1935 = 3^{2} \cdot 5 \cdot 43 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1935.b (of order \(2\) and degree \(1\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 5 \)
Character field:			\(\Q\)
Newform subspaces:			\( 7 \)
Sturm bound:			\(528\)
Trace bound:			\(5\)
Distinguishing \(T_p\):			\(2\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(1935, [\chi])\).

	Total	New	Old
Modular forms	272	104	168
Cusp forms	256	104	152
Eisenstein series	16	0	16

Trace form

104 * q - 98 * q^4 - 10 * q^10 + 8 * q^11 + 86 * q^16 + 4 * q^19 + 16 * q^25 - 24 * q^26 - 24 * q^31 - 44 * q^34 + 12 * q^35 + 50 * q^40 + 12 * q^41 + 24 * q^46 - 124 * q^49 - 12 * q^50 - 8 * q^55 - 2 * q^56 - 32 * q^59 - 4 * q^61 - 86 * q^64 - 12 * q^65 - 12 * q^70 - 40 * q^71 + 42 * q^74 - 56 * q^76 + 40 * q^79 - 16 * q^80 + 8 * q^85 + 10 * q^86 + 20 * q^89 + 64 * q^91 + 68 * q^94 + 12 * q^95

Decomposition of \(S_{2}^{\mathrm{new}}(1935, [\chi])\) 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
																		$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
1935.2.b.a	$1935$	$2$	1935.b	5.b	$2$	$4$	$4$	$15.451$	\(\Q(\zeta_{12})\)	None					645.2.b.b	$2$	$0$	\(0\)	\(0\)	\(-2\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+(-1+2\zeta_{12}^{2})q^{2}-q^{4}+(-1+2\zeta_{12}+\cdots)q^{5}+\cdots\)
1935.2.b.b	$1935$	$2$	1935.b	5.b	$2$	$4$	$4$	$15.451$	\(\Q(\zeta_{8})\)	None					645.2.b.a	$2$	$0$	\(0\)	\(0\)	\(4\)	\(0\)	$2$	$\mathrm{SU}(2)[C_{2}]$	\(q+(\beta_{2}+\beta_1)q^{2}+(-2\beta_{3}-1)q^{4}+\cdots\)
1935.2.b.c	$1935$	$2$	1935.b	5.b	$2$	$6$	$6$	$15.451$	6.0.1827904.1	None					215.2.b.a	$2$	$0$	\(0\)	\(0\)	\(12\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta _{1}q^{2}+(-1-\beta _{2}+\beta _{3})q^{4}+(2+\beta _{4}+\cdots)q^{5}+\cdots\)
1935.2.b.d	$1935$	$2$	1935.b	5.b	$2$	$14$	$14$	$15.451$	\(\mathbb{Q}[x]/(x^{14} + \cdots)\)	None					215.2.b.b	$2$	$0$	\(0\)	\(0\)	\(-8\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+(\beta _{1}+\beta _{9})q^{2}+(-1+\beta _{4}+\beta _{8})q^{4}+\cdots\)
1935.2.b.e	$1935$	$2$	1935.b	5.b	$2$	$16$	$16$	$15.451$	\(\mathbb{Q}[x]/(x^{16} + \cdots)\)	None					645.2.b.c	$2$	$0$	\(0\)	\(0\)	\(-2\)	\(0\)	$2^{3}$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta _{1}q^{2}+\beta _{2}q^{4}+(\beta _{3}+\beta _{10})q^{5}+(\beta _{12}+\cdots)q^{7}+\cdots\)
1935.2.b.f	$1935$	$2$	1935.b	5.b	$2$	$20$	$20$	$15.451$	\(\mathbb{Q}[x]/(x^{20} + \cdots)\)	None					645.2.b.d	$2$	$0$	\(0\)	\(0\)	\(-4\)	\(0\)	$2^{4}$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta _{1}q^{2}+(-2+\beta _{2}-\beta _{3})q^{4}+\beta _{8}q^{5}+\cdots\)
1935.2.b.g	$1935$	$2$	1935.b	5.b	$2$	$40$	$40$	$15.451$		None		✓	✓		1935.2.b.g	$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)		$\mathrm{SU}(2)[C_{2}]$

Decomposition of \(S_{2}^{\mathrm{old}}(1935, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(1935, [\chi]) \simeq \) \(S_{2}^{\mathrm{new}}(45, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(215, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(645, [\chi])\)\(^{\oplus 2}\)