Space of modular forms of level 1204, weight 2, and trivial character

• Label: 1204.2.a
• Level: $1204$
• Weight: $2$
• Character orbit: 1204.a
• Rep. character: $\chi_{1204}(1,\cdot)$
• Character field: $\Q$
• Dimension: $22$
• Newform subspaces: $5$
• Sturm bound: $352$
• Trace bound: $3$

Defining parameters

Level:	\( N \)	\(=\)	\( 1204 = 2^{2} \cdot 7 \cdot 43 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1204.a (trivial)
Character field:			\(\Q\)
Newform subspaces:			\( 5 \)
Sturm bound:			\(352\)
Trace bound:			\(3\)
Distinguishing \(T_p\):			\(3\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_0(1204))\).

	Total	New	Old
Modular forms	182	22	160
Cusp forms	171	22	149
Eisenstein series	11	0	11

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

\(2\)	\(7\)	\(43\)	Fricke	Dim
\(-\)	\(+\)	\(+\)	$-$	\(6\)
\(-\)	\(+\)	\(-\)	$+$	\(5\)
\(-\)	\(-\)	\(+\)	$+$	\(4\)
\(-\)	\(-\)	\(-\)	$-$	\(7\)
Plus space			\(+\)	\(9\)
Minus space			\(-\)	\(13\)

Trace form

\( 22 q - 4 q^{3} + 18 q^{9} + O(q^{10}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(1204))\) into newform subspaces

Label	Level	Weight	Char	Prim	Char order	Dim	Rel. Dim	$A$	Field	CM	Self-dual	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	7	43
1204.2.a.a	$1204$	$2$	1204.a	1.a	$1$	$1$	$1$	$9.614$	\(\Q\)	None	✓	$1$	$1$	\(0\)	\(2\)	\(-4\)	\(-1\)		$-$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q+2q^{3}-4q^{5}-q^{7}+q^{9}+5q^{11}+\cdots\)
1204.2.a.b	$1204$	$2$	1204.a	1.a	$1$	$4$	$4$	$9.614$	4.4.3981.1	None	✓	$1$	$1$	\(0\)	\(-3\)	\(-2\)	\(-4\)		$-$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q+(-1-\beta _{3})q^{3}+(-1+\beta _{1}-\beta _{3})q^{5}+\cdots\)
1204.2.a.c	$1204$	$2$	1204.a	1.a	$1$	$4$	$4$	$9.614$	\(\Q(\zeta_{15})^+\)	None	✓	$1$	$1$	\(0\)	\(-1\)	\(-4\)	\(4\)		$-$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q+(\beta _{2}+\beta _{3})q^{3}+(-\beta _{1}-\beta _{2}+\beta _{3})q^{5}+\cdots\)
1204.2.a.d	$1204$	$2$	1204.a	1.a	$1$	$6$	$6$	$9.614$	\(\mathbb{Q}[x]/(x^{6} - \cdots)\)	None	✓	$1$	$0$	\(0\)	\(-1\)	\(4\)	\(-6\)		$-$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q-\beta _{1}q^{3}+(1-\beta _{3})q^{5}-q^{7}+(1-\beta _{4}+\cdots)q^{9}+\cdots\)
1204.2.a.e	$1204$	$2$	1204.a	1.a	$1$	$7$	$7$	$9.614$	\(\mathbb{Q}[x]/(x^{7} - \cdots)\)	None	✓	$1$	$0$	\(0\)	\(-1\)	\(6\)	\(7\)		$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q-\beta _{1}q^{3}+(1-\beta _{2})q^{5}+q^{7}+(2-\beta _{3}+\cdots)q^{9}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_0(1204))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_0(1204)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_0(14))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(28))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(43))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(86))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(172))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(301))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(602))\)\(^{\oplus 2}\)