Space of modular forms of level 1500, weight 2, and Character 1500.o

• Label: 1500.2.o
• Level: $1500$
• Weight: $2$
• Character orbit: 1500.o
• Rep. character: $\chi_{1500}(49,\cdot)$
• Character field: $\Q(\zeta_{10})$
• Dimension: $56$
• Newform subspaces: $3$
• Sturm bound: $600$
• Trace bound: $11$

Defining parameters

Level:	\( N \)	\(=\)	\( 1500 = 2^{2} \cdot 3 \cdot 5^{3} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1500.o (of order \(10\) and degree \(4\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 25 \)
Character field:			\(\Q(\zeta_{10})\)
Newform subspaces:			\( 3 \)
Sturm bound:			\(600\)
Trace bound:			\(11\)
Distinguishing \(T_p\):			\(7\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(1500, [\chi])\).

	Total	New	Old
Modular forms	1320	56	1264
Cusp forms	1080	56	1024
Eisenstein series	240	0	240

Trace form

56 * q + 14 * q^9 + 6 * q^11 - 10 * q^17 - 10 * q^19 + 4 * q^21 - 40 * q^23 - 44 * q^29 - 6 * q^31 - 10 * q^33 + 50 * q^41 + 40 * q^47 - 24 * q^49 - 16 * q^51 + 60 * q^53 + 36 * q^59 + 52 * q^61 + 10 * q^63 - 20 * q^67 - 4 * q^69 - 40 * q^71 - 60 * q^73 + 40 * q^77 - 8 * q^79 - 14 * q^81 + 50 * q^83 + 20 * q^87 + 60 * q^89 + 30 * q^91 + 40 * q^97 + 4 * q^99

Decomposition of \(S_{2}^{\mathrm{new}}(1500, [\chi])\) 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
																		$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
1500.2.o.a	$1500$	$2$	1500.o	25.e	$10$	$16$	$4$	$11.978$	\(\Q(\zeta_{60})\)	None					300.2.m.a	$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$5^{2}$	$\mathrm{SU}(2)[C_{10}]$	\(q+\beta_{4} q^{3}+(-\beta_{14}-\beta_{12}+\cdots-\beta_1)q^{7}+\cdots\)
1500.2.o.b	$1500$	$2$	1500.o	25.e	$10$	$16$	$4$	$11.978$	16.0.\(\cdots\).9	None					300.2.m.b	$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$5^{2}$	$\mathrm{SU}(2)[C_{10}]$	\(q-\beta _{6}q^{3}+(\beta _{1}+\beta _{3}+\beta _{6}+\beta _{10}+2\beta _{13}+\cdots)q^{7}+\cdots\)
1500.2.o.c	$1500$	$2$	1500.o	25.e	$10$	$24$	$6$	$11.978$		None			✓		300.2.o.a	$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)		$\mathrm{SU}(2)[C_{10}]$

Decomposition of \(S_{2}^{\mathrm{old}}(1500, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(1500, [\chi]) \simeq \) \(S_{2}^{\mathrm{new}}(25, [\chi])\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(50, [\chi])\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(75, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(100, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(125, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(150, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(250, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(300, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(375, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(500, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(750, [\chi])\)\(^{\oplus 2}\)