Space of modular forms of level 2900, weight 2, and trivial character

• Label: 2900.2.a
• Level: $2900$
• Weight: $2$
• Character orbit: 2900.a
• Rep. character: $\chi_{2900}(1,\cdot)$
• Character field: $\Q$
• Dimension: $45$
• Newform subspaces: $13$
• Sturm bound: $900$
• Trace bound: $9$

Defining parameters

Level:	\( N \)	\(=\)	\( 2900 = 2^{2} \cdot 5^{2} \cdot 29 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	2900.a (trivial)
Character field:			\(\Q\)
Newform subspaces:			\( 13 \)
Sturm bound:			\(900\)
Trace bound:			\(9\)
Distinguishing \(T_p\):			\(3\), \(7\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_0(2900))\).

	Total	New	Old
Modular forms	468	45	423
Cusp forms	433	45	388
Eisenstein series	35	0	35

The following table gives the dimensions of the cuspidal new subspaces with specified eigenvalues for the Atkin-Lehner operators and the Fricke involution.

\(2\)	\(5\)	\(29\)	Fricke		Total				Cusp				Eisenstein
					All	New	Old		All	New	Old		All	New	Old
\(+\)	\(+\)	\(+\)	\(+\)		\(54\)	\(0\)	\(54\)		\(49\)	\(0\)	\(49\)		\(5\)	\(0\)	\(5\)
\(+\)	\(+\)	\(-\)	\(-\)		\(63\)	\(0\)	\(63\)		\(57\)	\(0\)	\(57\)		\(6\)	\(0\)	\(6\)
\(+\)	\(-\)	\(+\)	\(-\)		\(61\)	\(0\)	\(61\)		\(55\)	\(0\)	\(55\)		\(6\)	\(0\)	\(6\)
\(+\)	\(-\)	\(-\)	\(+\)		\(58\)	\(0\)	\(58\)		\(52\)	\(0\)	\(52\)		\(6\)	\(0\)	\(6\)
\(-\)	\(+\)	\(+\)	\(-\)		\(63\)	\(12\)	\(51\)		\(60\)	\(12\)	\(48\)		\(3\)	\(0\)	\(3\)
\(-\)	\(+\)	\(-\)	\(+\)		\(54\)	\(9\)	\(45\)		\(51\)	\(9\)	\(42\)		\(3\)	\(0\)	\(3\)
\(-\)	\(-\)	\(+\)	\(+\)		\(56\)	\(9\)	\(47\)		\(53\)	\(9\)	\(44\)		\(3\)	\(0\)	\(3\)
\(-\)	\(-\)	\(-\)	\(-\)		\(59\)	\(15\)	\(44\)		\(56\)	\(15\)	\(41\)		\(3\)	\(0\)	\(3\)
Plus space			\(+\)		\(222\)	\(18\)	\(204\)		\(205\)	\(18\)	\(187\)		\(17\)	\(0\)	\(17\)
Minus space			\(-\)		\(246\)	\(27\)	\(219\)		\(228\)	\(27\)	\(201\)		\(18\)	\(0\)	\(18\)

Trace form

45 * q - 4 * q^3 + 43 * q^9 + 4 * q^11 + 4 * q^13 - 6 * q^17 + 10 * q^19 + 4 * q^21 + 12 * q^23 + 2 * q^27 + 3 * q^29 - 18 * q^33 + 6 * q^37 + 2 * q^39 + 2 * q^41 - 16 * q^43 + 8 * q^47 + 45 * q^49 - 28 * q^51 - 16 * q^53 + 36 * q^57 - 48 * q^59 + 10 * q^61 - 16 * q^63 + 8 * q^67 + 4 * q^69 + 40 * q^71 - 6 * q^73 + 4 * q^77 - 12 * q^79 + 49 * q^81 - 16 * q^83 + 30 * q^89 + 36 * q^91 + 18 * q^93 + 18 * q^97 - 10 * q^99

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(2900))\) 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					A-L signs			Fricke sign	Coefficient ring index	Sato-Tate	$q$-expansion
																		$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$		2	5	29
2900.2.a.a	$2900$	$2$	2900.a	1.a	$1$	$1$	$1$	$23.157$	\(\Q\)	None	✓				116.2.a.c	$1$	$2$	\(0\)	\(-2\)	\(0\)	\(-4\)		$-$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q-2q^{3}-4q^{7}+q^{9}-6q^{11}-2q^{13}+\cdots\)
2900.2.a.b	$2900$	$2$	2900.a	1.a	$1$	$1$	$1$	$23.157$	\(\Q\)	None	✓				116.2.a.b	$1$	$0$	\(0\)	\(-1\)	\(0\)	\(4\)		$-$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q-q^{3}+4q^{7}-2q^{9}+3q^{11}-5q^{13}+\cdots\)
2900.2.a.c	$2900$	$2$	2900.a	1.a	$1$	$1$	$1$	$23.157$	\(\Q\)	None	✓				580.2.a.a	$1$	$1$	\(0\)	\(0\)	\(0\)	\(0\)		$-$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q-3q^{9}-2q^{11}+2q^{13}-2q^{19}+8q^{23}+\cdots\)
2900.2.a.d	$2900$	$2$	2900.a	1.a	$1$	$1$	$1$	$23.157$	\(\Q\)	None	✓				580.2.a.b	$1$	$0$	\(0\)	\(0\)	\(0\)	\(2\)		$-$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+2q^{7}-3q^{9}-4q^{11}+6q^{13}+4q^{17}+\cdots\)
2900.2.a.e	$2900$	$2$	2900.a	1.a	$1$	$1$	$1$	$23.157$	\(\Q\)	None	✓				116.2.a.a	$1$	$0$	\(0\)	\(3\)	\(0\)	\(-4\)		$-$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+3q^{3}-4q^{7}+6q^{9}-q^{11}+3q^{13}+\cdots\)
2900.2.a.f	$2900$	$2$	2900.a	1.a	$1$	$3$	$3$	$23.157$	3.3.148.1	None	✓				580.2.a.d	$1$	$1$	\(0\)	\(-2\)	\(0\)	\(-2\)		$-$	$+$	$-$	$+$	$2$	$\mathrm{SU}(2)$	\(q+(-1+\beta _{1})q^{3}+(-1+\beta _{2})q^{7}+(1+\cdots)q^{9}+\cdots\)
2900.2.a.g	$2900$	$2$	2900.a	1.a	$1$	$3$	$3$	$23.157$	3.3.564.1	None	✓				580.2.a.c	$1$	$0$	\(0\)	\(-2\)	\(0\)	\(4\)		$-$	$+$	$+$	$-$	$2$	$\mathrm{SU}(2)$	\(q+(-1-\beta _{2})q^{3}+(1-\beta _{2})q^{7}+(4+\beta _{1}+\cdots)q^{9}+\cdots\)
2900.2.a.h	$2900$	$2$	2900.a	1.a	$1$	$4$	$4$	$23.157$	\(\Q(\zeta_{24})^+\)	None	✓				580.2.c.a	$2$	$1$	\(0\)	\(0\)	\(0\)	\(0\)		$-$	$-$	$+$	$+$	$2$	$\mathrm{SU}(2)$	\(q-\beta _{2}q^{3}+\beta _{2}q^{7}-q^{9}+(-1-\beta _{1}+\cdots)q^{11}+\cdots\)
2900.2.a.i	$2900$	$2$	2900.a	1.a	$1$	$5$	$5$	$23.157$	5.5.2370465.1	None	✓	✓	✓		2900.2.a.i	$1$	$1$	\(0\)	\(0\)	\(0\)	\(-4\)		$-$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q+\beta _{1}q^{3}+(-1+\beta _{4})q^{7}+(1+\beta _{2}-\beta _{3}+\cdots)q^{9}+\cdots\)
2900.2.a.j	$2900$	$2$	2900.a	1.a	$1$	$5$	$5$	$23.157$	5.5.3076177.1	None	✓	✓	✓		2900.2.a.j	$1$	$1$	\(0\)	\(0\)	\(0\)	\(-4\)		$-$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q-\beta _{1}q^{3}+(\beta _{1}-\beta _{2}+\beta _{3})q^{7}+(1+\beta _{2}+\cdots)q^{9}+\cdots\)
2900.2.a.k	$2900$	$2$	2900.a	1.a	$1$	$5$	$5$	$23.157$	5.5.2370465.1	None	✓	✓	✓		2900.2.a.i	$1$	$0$	\(0\)	\(0\)	\(0\)	\(4\)		$-$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q-\beta _{1}q^{3}+(1-\beta _{4})q^{7}+(1+\beta _{2}-\beta _{3}+\cdots)q^{9}+\cdots\)
2900.2.a.l	$2900$	$2$	2900.a	1.a	$1$	$5$	$5$	$23.157$	5.5.3076177.1	None	✓	✓			2900.2.a.j	$1$	$0$	\(0\)	\(0\)	\(0\)	\(4\)		$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+\beta _{1}q^{3}+(-\beta _{1}+\beta _{2}-\beta _{3})q^{7}+(1+\cdots)q^{9}+\cdots\)
2900.2.a.m	$2900$	$2$	2900.a	1.a	$1$	$10$	$10$	$23.157$	\(\mathbb{Q}[x]/(x^{10} - \cdots)\)	None	✓		✓		580.2.c.b	$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)		$-$	$-$	$-$	$-$	$2^{4}$	$\mathrm{SU}(2)$	\(q+\beta _{1}q^{3}+(\beta _{1}-\beta _{9})q^{7}+(1+\beta _{2})q^{9}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_0(2900))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_0(2900)) \simeq \) \(S_{2}^{\mathrm{new}}(\Gamma_0(20))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(29))\)\(^{\oplus 9}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(50))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(58))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(100))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(116))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(145))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(290))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(580))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(725))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(1450))\)\(^{\oplus 2}\)