Space of modular forms of level 3060, weight 2, and Character 3060.e

• Label: 3060.2.e
• Level: $3060$
• Weight: $2$
• Character orbit: 3060.e
• Rep. character: $\chi_{3060}(1801,\cdot)$
• Character field: $\Q$
• Dimension: $30$
• Newform subspaces: $10$
• Sturm bound: $1296$
• Trace bound: $19$

Defining parameters

Level:	\( N \)	\(=\)	\( 3060 = 2^{2} \cdot 3^{2} \cdot 5 \cdot 17 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	3060.e (of order \(2\) and degree \(1\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 17 \)
Character field:			\(\Q\)
Newform subspaces:			\( 10 \)
Sturm bound:			\(1296\)
Trace bound:			\(19\)
Distinguishing \(T_p\):			\(7\), \(11\), \(47\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(3060, [\chi])\).

	Total	New	Old
Modular forms	672	30	642
Cusp forms	624	30	594
Eisenstein series	48	0	48

Trace form

\( 30 q - 6 q^{17} + 16 q^{19} - 30 q^{25} - 16 q^{47} - 70 q^{49} - 28 q^{53} - 16 q^{55} - 16 q^{59} + 24 q^{67} - 52 q^{77} + 16 q^{83} - 4 q^{85} + 4 q^{89}+O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(3060, [\chi])\) 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
																		$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
3060.2.e.a	$3060$	$2$	3060.e	17.b	$2$	$2$	$2$	$24.434$	\(\Q(\sqrt{-1}) \)	None					1020.2.e.a	$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+i q^{5}+2 i q^{11}-6 q^{13}+(-i+4)q^{17}+\cdots\)
3060.2.e.b	$3060$	$2$	3060.e	17.b	$2$	$2$	$2$	$24.434$	\(\Q(\sqrt{-1}) \)	None		✓			3060.2.e.b	$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+i q^{5}-2 q^{13}+(i-4)q^{17}-4 i q^{23}+\cdots\)
3060.2.e.c	$3060$	$2$	3060.e	17.b	$2$	$2$	$2$	$24.434$	\(\Q(\sqrt{-1}) \)	None		✓			3060.2.e.c	$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+i q^{5}+5 i q^{7}+5 i q^{11}-2 q^{13}+\cdots\)
3060.2.e.d	$3060$	$2$	3060.e	17.b	$2$	$2$	$2$	$24.434$	\(\Q(\sqrt{-1}) \)	None					1020.2.e.b	$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+i q^{5}+3 i q^{7}+3 i q^{11}-2 q^{13}+\cdots\)
3060.2.e.e	$3060$	$2$	3060.e	17.b	$2$	$2$	$2$	$24.434$	\(\Q(\sqrt{-1}) \)	None		✓			3060.2.e.c	$2$	$1$	\(0\)	\(0\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q-i q^{5}+5 i q^{7}-5 i q^{11}-2 q^{13}+\cdots\)
3060.2.e.f	$3060$	$2$	3060.e	17.b	$2$	$2$	$2$	$24.434$	\(\Q(\sqrt{-1}) \)	None		✓			3060.2.e.b	$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q-i q^{5}-2 q^{13}+(-i+4)q^{17}+4 i q^{23}+\cdots\)
3060.2.e.g	$3060$	$2$	3060.e	17.b	$2$	$4$	$4$	$24.434$	\(\Q(\zeta_{8})\)	None					1020.2.e.d	$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2^{3}$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta_1 q^{5}+(\beta_{2}+\beta_1)q^{7}+(\beta_{2}+3\beta_1)q^{11}+\cdots\)
3060.2.e.h	$3060$	$2$	3060.e	17.b	$2$	$4$	$4$	$24.434$	\(\Q(i, \sqrt{33})\)	None					1020.2.e.c	$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta _{2}q^{5}+\beta _{1}q^{7}+(-\beta _{1}-2\beta _{2})q^{11}+\cdots\)
3060.2.e.i	$3060$	$2$	3060.e	17.b	$2$	$4$	$4$	$24.434$	\(\Q(i, \sqrt{13})\)	None		✓			3060.2.e.i	$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2^{2}$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta _{1}q^{5}+\beta _{2}q^{7}-\beta _{1}q^{11}+4q^{13}+\cdots\)
3060.2.e.j	$3060$	$2$	3060.e	17.b	$2$	$6$	$6$	$24.434$	6.0.37161216.1	None			✓		340.2.c.a	$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2$	$\mathrm{SU}(2)[C_{2}]$	\(q-\beta _{4}q^{5}+(\beta _{1}+\beta _{4})q^{7}+(3\beta _{4}-\beta _{5})q^{11}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(3060, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(3060, [\chi]) \simeq \) \(S_{2}^{\mathrm{new}}(34, [\chi])\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(51, [\chi])\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(68, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(85, [\chi])\)\(^{\oplus 9}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(102, [\chi])\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(153, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(170, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(204, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(255, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(306, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(340, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(510, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(612, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(765, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(1020, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(1530, [\chi])\)\(^{\oplus 2}\)