Space of modular forms of level 1900, weight 2, and Character 1900.i

• Label: 1900.2.i
• Level: $1900$
• Weight: $2$
• Character orbit: 1900.i
• Rep. character: $\chi_{1900}(201,\cdot)$
• Character field: $\Q(\zeta_{3})$
• Dimension: $62$
• Newform subspaces: $7$
• Sturm bound: $600$
• Trace bound: $3$

Defining parameters

Level:	\( N \)	\(=\)	\( 1900 = 2^{2} \cdot 5^{2} \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1900.i (of order \(3\) and degree \(2\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 19 \)
Character field:			\(\Q(\zeta_{3})\)
Newform subspaces:			\( 7 \)
Sturm bound:			\(600\)
Trace bound:			\(3\)
Distinguishing \(T_p\):			\(3\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(1900, [\chi])\).

	Total	New	Old
Modular forms	636	62	574
Cusp forms	564	62	502
Eisenstein series	72	0	72

Trace form

62 * q + q^3 + 4 * q^7 - 28 * q^9 + 4 * q^11 - 7 * q^13 + q^17 - 12 * q^19 - 6 * q^21 - 5 * q^23 - 2 * q^27 + 9 * q^29 + 12 * q^31 - 12 * q^33 + 36 * q^37 + 54 * q^39 + q^41 - 17 * q^43 - 23 * q^47 + 78 * q^49 + 35 * q^51 - 13 * q^53 - 35 * q^57 + 11 * q^59 - 7 * q^61 - 6 * q^63 - 13 * q^67 - 34 * q^69 + 11 * q^71 + 13 * q^73 - 20 * q^77 + 13 * q^79 - 7 * q^81 + 20 * q^83 + 26 * q^87 + 7 * q^89 - 18 * q^91 + 19 * q^97

Decomposition of \(S_{2}^{\mathrm{new}}(1900, [\chi])\) 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
																		$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
1900.2.i.a	$1900$	$2$	1900.i	19.c	$3$	$2$	$1$	$15.172$	\(\Q(\sqrt{-3}) \)	None					76.2.e.a	$2$	$1$	\(0\)	\(-1\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{3}]$	\(q+(-1+\zeta_{6})q^{3}+2\zeta_{6}q^{9}-4q^{11}+\cdots\)
1900.2.i.b	$1900$	$2$	1900.i	19.c	$3$	$2$	$1$	$15.172$	\(\Q(\sqrt{-3}) \)	None					380.2.i.a	$2$	$0$	\(0\)	\(2\)	\(0\)	\(8\)	$1$	$\mathrm{SU}(2)[C_{3}]$	\(q+(2-2\zeta_{6})q^{3}+4q^{7}-\zeta_{6}q^{9}-3q^{11}+\cdots\)
1900.2.i.c	$1900$	$2$	1900.i	19.c	$3$	$6$	$3$	$15.172$	6.0.1783323.2	None					380.2.i.b	$2$	$0$	\(0\)	\(-1\)	\(0\)	\(-4\)	$3$	$\mathrm{SU}(2)[C_{3}]$	\(q+(-\beta _{3}+\beta _{5})q^{3}+(-1+\beta _{3})q^{7}+(\beta _{1}+\cdots)q^{9}+\cdots\)
1900.2.i.d	$1900$	$2$	1900.i	19.c	$3$	$8$	$4$	$15.172$	\(\mathbb{Q}[x]/(x^{8} - \cdots)\)	None					380.2.i.c	$2$	$0$	\(0\)	\(1\)	\(0\)	\(0\)	$3$	$\mathrm{SU}(2)[C_{3}]$	\(q+\beta _{1}q^{3}-\beta _{7}q^{7}+(-1+\beta _{1}+\beta _{2}+\cdots)q^{9}+\cdots\)
1900.2.i.e	$1900$	$2$	1900.i	19.c	$3$	$12$	$6$	$15.172$	\(\mathbb{Q}[x]/(x^{12} - \cdots)\)	None		✓			1900.2.i.e	$2$	$0$	\(0\)	\(-3\)	\(0\)	\(0\)	$3$	$\mathrm{SU}(2)[C_{3}]$	\(q+(-1+\beta _{1}-\beta _{6})q^{3}+\beta _{4}q^{7}+(1-\beta _{1}+\cdots)q^{9}+\cdots\)
1900.2.i.f	$1900$	$2$	1900.i	19.c	$3$	$12$	$6$	$15.172$	\(\mathbb{Q}[x]/(x^{12} - \cdots)\)	None		✓			1900.2.i.e	$2$	$0$	\(0\)	\(3\)	\(0\)	\(0\)	$3$	$\mathrm{SU}(2)[C_{3}]$	\(q+(1-\beta _{1}+\beta _{6})q^{3}-\beta _{4}q^{7}+(1-\beta _{1}+\cdots)q^{9}+\cdots\)
1900.2.i.g	$1900$	$2$	1900.i	19.c	$3$	$20$	$10$	$15.172$	\(\mathbb{Q}[x]/(x^{20} + \cdots)\)	None			✓		380.2.r.a	$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2^{2}$	$\mathrm{SU}(2)[C_{3}]$	\(q+\beta _{14}q^{3}+(\beta _{15}+\beta _{18})q^{7}+(-1+\beta _{4}+\cdots)q^{9}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(1900, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(1900, [\chi]) \simeq \) \(S_{2}^{\mathrm{new}}(38, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(76, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(95, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(190, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(380, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(475, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(950, [\chi])\)\(^{\oplus 2}\)