Space of modular forms of level 1260, weight 2, and Character 1260.k

• Label: 1260.2.k
• Level: $1260$
• Weight: $2$
• Character orbit: 1260.k
• Rep. character: $\chi_{1260}(1009,\cdot)$
• Character field: $\Q$
• Dimension: $16$
• Newform subspaces: $5$
• Sturm bound: $576$
• Trace bound: $11$

Defining parameters

Level:	\( N \)	\(=\)	\( 1260 = 2^{2} \cdot 3^{2} \cdot 5 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1260.k (of order \(2\) and degree \(1\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 5 \)
Character field:			\(\Q\)
Newform subspaces:			\( 5 \)
Sturm bound:			\(576\)
Trace bound:			\(11\)
Distinguishing \(T_p\):			\(11\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(1260, [\chi])\).

	Total	New	Old
Modular forms	312	16	296
Cusp forms	264	16	248
Eisenstein series	48	0	48

Trace form

16 * q + 2 * q^5 - 6 * q^11 - 8 * q^19 + 12 * q^25 + 26 * q^29 - 4 * q^31 - 2 * q^35 - 16 * q^41 - 16 * q^49 - 4 * q^55 - 12 * q^59 + 12 * q^61 - 22 * q^65 - 8 * q^71 - 26 * q^79 - 10 * q^85 + 44 * q^89 + 10 * q^91 + 8 * q^95

Decomposition of \(S_{2}^{\mathrm{new}}(1260, [\chi])\) 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
																		$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
1260.2.k.a	$1260$	$2$	1260.k	5.b	$2$	$2$	$2$	$10.061$	\(\Q(\sqrt{-1}) \)	None					420.2.k.b	$2$	$0$	\(0\)	\(0\)	\(-4\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+(-i-2)q^{5}-i q^{7}-4 q^{11}+2 i q^{13}+\cdots\)
1260.2.k.b	$1260$	$2$	1260.k	5.b	$2$	$2$	$2$	$10.061$	\(\Q(\sqrt{-1}) \)	None					140.2.e.b	$2$	$0$	\(0\)	\(0\)	\(-2\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+(-2 i-1)q^{5}+i q^{7}-4 i q^{13}+\cdots\)
1260.2.k.c	$1260$	$2$	1260.k	5.b	$2$	$2$	$2$	$10.061$	\(\Q(\sqrt{-1}) \)	None					140.2.e.a	$2$	$0$	\(0\)	\(0\)	\(4\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+(i+2)q^{5}+i q^{7}-3 q^{11}-i q^{13}+\cdots\)
1260.2.k.d	$1260$	$2$	1260.k	5.b	$2$	$2$	$2$	$10.061$	\(\Q(\sqrt{-1}) \)	None					420.2.k.a	$2$	$0$	\(0\)	\(0\)	\(4\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+(-i+2)q^{5}-i q^{7}+4 q^{11}-6 i q^{13}+\cdots\)
1260.2.k.e	$1260$	$2$	1260.k	5.b	$2$	$8$	$8$	$10.061$	8.0.49787136.1	None		✓	✓		1260.2.k.e	$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2^{8}$	$\mathrm{SU}(2)[C_{2}]$	\(q-\beta _{7}q^{5}-\beta _{1}q^{7}+(\beta _{3}+\beta _{4}+\beta _{5}+\beta _{7})q^{11}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(1260, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(1260, [\chi]) \simeq \) \(S_{2}^{\mathrm{new}}(30, [\chi])\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(35, [\chi])\)\(^{\oplus 9}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(45, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(60, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(70, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(90, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(105, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(140, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(180, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(210, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(315, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(420, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(630, [\chi])\)\(^{\oplus 2}\)