Space of modular forms of level 3267, weight 2, and trivial character

• Label: 3267.2.a
• Level: $3267$
• Weight: $2$
• Character orbit: 3267.a
• Rep. character: $\chi_{3267}(1,\cdot)$
• Character field: $\Q$
• Dimension: $145$
• Newform subspaces: $39$
• Sturm bound: $792$
• Trace bound: $31$

Defining parameters

Level:	\( N \)	\(=\)	\( 3267 = 3^{3} \cdot 11^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	3267.a (trivial)
Character field:			\(\Q\)
Newform subspaces:			\( 39 \)
Sturm bound:			\(792\)
Trace bound:			\(31\)
Distinguishing \(T_p\):			\(2\), \(5\), \(7\), \(23\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_0(3267))\).

	Total	New	Old
Modular forms	432	145	287
Cusp forms	361	145	216
Eisenstein series	71	0	71

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

\(3\)	\(11\)	Fricke		Total				Cusp				Eisenstein
				All	New	Old		All	New	Old		All	New	Old
\(+\)	\(+\)	\(+\)		\(102\)	\(32\)	\(70\)		\(85\)	\(32\)	\(53\)		\(17\)	\(0\)	\(17\)
\(+\)	\(-\)	\(-\)		\(114\)	\(40\)	\(74\)		\(96\)	\(40\)	\(56\)		\(18\)	\(0\)	\(18\)
\(-\)	\(+\)	\(-\)		\(114\)	\(40\)	\(74\)		\(96\)	\(40\)	\(56\)		\(18\)	\(0\)	\(18\)
\(-\)	\(-\)	\(+\)		\(102\)	\(33\)	\(69\)		\(84\)	\(33\)	\(51\)		\(18\)	\(0\)	\(18\)
Plus space		\(+\)		\(204\)	\(65\)	\(139\)		\(169\)	\(65\)	\(104\)		\(35\)	\(0\)	\(35\)
Minus space		\(-\)		\(228\)	\(80\)	\(148\)		\(192\)	\(80\)	\(112\)		\(36\)	\(0\)	\(36\)

Trace form

145 * q + 142 * q^4 + 3 * q^7 + 12 * q^10 + 9 * q^13 + 124 * q^16 - 3 * q^19 + 163 * q^25 - 6 * q^28 + 12 * q^31 + 28 * q^34 + 31 * q^37 + 36 * q^40 + 134 * q^49 + 42 * q^52 - 8 * q^58 + 27 * q^61 + 148 * q^64 - 19 * q^67 + 44 * q^70 - 15 * q^73 + 90 * q^76 - 63 * q^79 + 84 * q^82 + 12 * q^85 - 49 * q^91 - 60 * q^94 - 35 * q^97

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(3267))\) 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
																		$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$		3	11
3267.2.a.a	$3267$	$2$	3267.a	1.a	$1$	$1$	$1$	$26.087$	\(\Q\)	None	✓				297.2.a.a	$1$	$1$	\(-2\)	\(0\)	\(2\)	\(-1\)		$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q-2q^{2}+2q^{4}+2q^{5}-q^{7}-4q^{10}+\cdots\)
3267.2.a.b	$3267$	$2$	3267.a	1.a	$1$	$1$	$1$	$26.087$	\(\Q\)	None	✓	✓			3267.2.a.b	$1$	$1$	\(-1\)	\(0\)	\(-2\)	\(-1\)		$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q-q^{2}-q^{4}-2q^{5}-q^{7}+3q^{8}+2q^{10}+\cdots\)
3267.2.a.c	$3267$	$2$	3267.a	1.a	$1$	$1$	$1$	$26.087$	\(\Q\)	None	✓				297.2.a.b	$1$	$1$	\(-1\)	\(0\)	\(-2\)	\(5\)		$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q-q^{2}-q^{4}-2q^{5}+5q^{7}+3q^{8}+2q^{10}+\cdots\)
3267.2.a.d	$3267$	$2$	3267.a	1.a	$1$	$1$	$1$	$26.087$	\(\Q\)	None	✓	✓			3267.2.a.b	$1$	$1$	\(-1\)	\(0\)	\(2\)	\(1\)		$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q-q^{2}-q^{4}+2q^{5}+q^{7}+3q^{8}-2q^{10}+\cdots\)
3267.2.a.e	$3267$	$2$	3267.a	1.a	$1$	$1$	$1$	$26.087$	\(\Q\)	\(\Q(\sqrt{-3}) \)	✓	✓			3267.2.a.e	$2$	$0$	\(0\)	\(0\)	\(0\)	\(-4\)		$+$	$-$	$-$	$1$	$N(\mathrm{U}(1))$	\(q-2q^{4}-4q^{7}-7q^{13}+4q^{16}-7q^{19}+\cdots\)
3267.2.a.f	$3267$	$2$	3267.a	1.a	$1$	$1$	$1$	$26.087$	\(\Q\)	\(\Q(\sqrt{-3}) \)	✓				27.2.a.a	$2$	$1$	\(0\)	\(0\)	\(0\)	\(1\)		$-$	$-$	$+$	$1$	$N(\mathrm{U}(1))$	\(q-2q^{4}+q^{7}-5q^{13}+4q^{16}+7q^{19}+\cdots\)
3267.2.a.g	$3267$	$2$	3267.a	1.a	$1$	$1$	$1$	$26.087$	\(\Q\)	\(\Q(\sqrt{-3}) \)	✓	✓			3267.2.a.e	$2$	$0$	\(0\)	\(0\)	\(0\)	\(4\)		$+$	$-$	$-$	$1$	$N(\mathrm{U}(1))$	\(q-2q^{4}+4q^{7}+7q^{13}+4q^{16}+7q^{19}+\cdots\)
3267.2.a.h	$3267$	$2$	3267.a	1.a	$1$	$1$	$1$	$26.087$	\(\Q\)	None	✓	✓			3267.2.a.b	$1$	$1$	\(1\)	\(0\)	\(-2\)	\(1\)		$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q+q^{2}-q^{4}-2q^{5}+q^{7}-3q^{8}-2q^{10}+\cdots\)
3267.2.a.i	$3267$	$2$	3267.a	1.a	$1$	$1$	$1$	$26.087$	\(\Q\)	None	✓	✓			3267.2.a.b	$1$	$1$	\(1\)	\(0\)	\(2\)	\(-1\)		$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q+q^{2}-q^{4}+2q^{5}-q^{7}-3q^{8}+2q^{10}+\cdots\)
3267.2.a.j	$3267$	$2$	3267.a	1.a	$1$	$1$	$1$	$26.087$	\(\Q\)	None	✓				297.2.a.b	$1$	$0$	\(1\)	\(0\)	\(2\)	\(5\)		$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+q^{2}-q^{4}+2q^{5}+5q^{7}-3q^{8}+2q^{10}+\cdots\)
3267.2.a.k	$3267$	$2$	3267.a	1.a	$1$	$1$	$1$	$26.087$	\(\Q\)	None	✓				297.2.a.a	$1$	$1$	\(2\)	\(0\)	\(-2\)	\(-1\)		$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q+2q^{2}+2q^{4}-2q^{5}-q^{7}-4q^{10}+\cdots\)
3267.2.a.l	$3267$	$2$	3267.a	1.a	$1$	$2$	$2$	$26.087$	\(\Q(\sqrt{3}) \)	None	✓				297.2.a.e	$1$	$0$	\(-2\)	\(0\)	\(2\)	\(4\)		$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+(-1+\beta )q^{2}+(2-2\beta )q^{4}+(1+\beta )q^{5}+\cdots\)
3267.2.a.m	$3267$	$2$	3267.a	1.a	$1$	$2$	$2$	$26.087$	\(\Q(\sqrt{3}) \)	\(\Q(\sqrt{-3}) \)	✓	✓			3267.2.a.m	$4$	$1$	\(0\)	\(0\)	\(0\)	\(0\)		$+$	$+$	$+$	$3$	$N(\mathrm{U}(1))$	\(q-2q^{4}-\beta q^{7}+\beta q^{13}+4q^{16}+\beta q^{19}+\cdots\)
3267.2.a.n	$3267$	$2$	3267.a	1.a	$1$	$2$	$2$	$26.087$	\(\Q(\sqrt{3}) \)	\(\Q(\sqrt{-3}) \)	✓	✓			3267.2.a.n	$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)		$-$	$+$	$-$	$1$	$N(\mathrm{U}(1))$	\(q-2q^{4}-2\beta q^{7}-\beta q^{13}+4q^{16}-3\beta q^{19}+\cdots\)
3267.2.a.o	$3267$	$2$	3267.a	1.a	$1$	$2$	$2$	$26.087$	\(\Q(\sqrt{3}) \)	None	✓	✓			3267.2.a.o	$2$	$1$	\(0\)	\(0\)	\(0\)	\(0\)		$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q+\beta q^{2}+q^{4}-\beta q^{7}-\beta q^{8}+\beta q^{13}+\cdots\)
3267.2.a.p	$3267$	$2$	3267.a	1.a	$1$	$2$	$2$	$26.087$	\(\Q(\sqrt{3}) \)	None	✓	✓			3267.2.a.o	$2$	$1$	\(0\)	\(0\)	\(0\)	\(0\)		$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q+\beta q^{2}+q^{4}+\beta q^{7}-\beta q^{8}-\beta q^{13}+\cdots\)
3267.2.a.q	$3267$	$2$	3267.a	1.a	$1$	$2$	$2$	$26.087$	\(\Q(\sqrt{3}) \)	None	✓				297.2.a.e	$1$	$0$	\(2\)	\(0\)	\(-2\)	\(4\)		$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+(1+\beta )q^{2}+(2+2\beta )q^{4}+(-1+\beta )q^{5}+\cdots\)
3267.2.a.r	$3267$	$2$	3267.a	1.a	$1$	$3$	$3$	$26.087$	3.3.321.1	None	✓	✓			3267.2.a.r	$1$	$1$	\(-1\)	\(0\)	\(-4\)	\(0\)		$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q-\beta _{1}q^{2}+(1+\beta _{1}+\beta _{2})q^{4}+(-1+\beta _{2})q^{5}+\cdots\)
3267.2.a.s	$3267$	$2$	3267.a	1.a	$1$	$3$	$3$	$26.087$	3.3.321.1	None	✓	✓			3267.2.a.r	$1$	$0$	\(-1\)	\(0\)	\(4\)	\(0\)		$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q-\beta _{1}q^{2}+(1+\beta _{1}+\beta _{2})q^{4}+(1-\beta _{2})q^{5}+\cdots\)
3267.2.a.t	$3267$	$2$	3267.a	1.a	$1$	$3$	$3$	$26.087$	3.3.564.1	None	✓				297.2.a.g	$1$	$1$	\(-1\)	\(0\)	\(-2\)	\(-7\)		$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q-\beta _{1}q^{2}+(2+\beta _{2})q^{4}+(-1-\beta _{2})q^{5}+\cdots\)
3267.2.a.u	$3267$	$2$	3267.a	1.a	$1$	$3$	$3$	$26.087$	3.3.321.1	None	✓	✓			3267.2.a.r	$1$	$1$	\(1\)	\(0\)	\(-4\)	\(0\)		$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q+\beta _{1}q^{2}+(1+\beta _{1}+\beta _{2})q^{4}+(-1+\beta _{2})q^{5}+\cdots\)
3267.2.a.v	$3267$	$2$	3267.a	1.a	$1$	$3$	$3$	$26.087$	3.3.321.1	None	✓	✓			3267.2.a.r	$1$	$0$	\(1\)	\(0\)	\(4\)	\(0\)		$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+\beta _{1}q^{2}+(1+\beta _{1}+\beta _{2})q^{4}+(1-\beta _{2})q^{5}+\cdots\)
3267.2.a.w	$3267$	$2$	3267.a	1.a	$1$	$3$	$3$	$26.087$	3.3.564.1	None	✓				297.2.a.g	$1$	$0$	\(1\)	\(0\)	\(2\)	\(-7\)		$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+\beta _{1}q^{2}+(2+\beta _{2})q^{4}+(1+\beta _{2})q^{5}+\cdots\)
3267.2.a.x	$3267$	$2$	3267.a	1.a	$1$	$4$	$4$	$26.087$	\(\Q(\sqrt{2}, \sqrt{5})\)	None	✓	✓			3267.2.a.x	$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)		$-$	$+$	$-$	$2^{2}$	$\mathrm{SU}(2)$	\(q+\beta _{1}q^{2}-\beta _{2}q^{5}-\beta _{3}q^{7}-2\beta _{1}q^{8}+\cdots\)
3267.2.a.y	$3267$	$2$	3267.a	1.a	$1$	$4$	$4$	$26.087$	\(\Q(\sqrt{2}, \sqrt{7})\)	None	✓	✓			3267.2.a.y	$2$	$1$	\(0\)	\(0\)	\(-4\)	\(0\)		$+$	$+$	$+$	$3$	$\mathrm{SU}(2)$	\(q+\beta _{1}q^{2}+(2+\beta _{2})q^{4}+(-1-\beta _{2})q^{5}+\cdots\)
3267.2.a.z	$3267$	$2$	3267.a	1.a	$1$	$4$	$4$	$26.087$	\(\Q(\sqrt{4 + \sqrt{3}})\)	None	✓	✓			3267.2.a.z	$2$	$0$	\(0\)	\(0\)	\(0\)	\(-4\)		$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+\beta _{1}q^{2}+(2+\beta _{2})q^{4}+\beta _{3}q^{5}+(-1+\cdots)q^{7}+\cdots\)
3267.2.a.ba	$3267$	$2$	3267.a	1.a	$1$	$4$	$4$	$26.087$	\(\Q(\sqrt{4 + \sqrt{3}})\)	None	✓	✓			3267.2.a.z	$2$	$0$	\(0\)	\(0\)	\(0\)	\(4\)		$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+\beta _{1}q^{2}+(2+\beta _{2})q^{4}-\beta _{3}q^{5}+(1-2\beta _{2}+\cdots)q^{7}+\cdots\)
3267.2.a.bb	$3267$	$2$	3267.a	1.a	$1$	$4$	$4$	$26.087$	\(\Q(\sqrt{2}, \sqrt{7})\)	None	✓	✓			3267.2.a.y	$2$	$0$	\(0\)	\(0\)	\(4\)	\(0\)		$-$	$+$	$-$	$3$	$\mathrm{SU}(2)$	\(q+\beta _{1}q^{2}+(2+\beta _{2})q^{4}+(1+\beta _{2})q^{5}+\cdots\)
3267.2.a.bc	$3267$	$2$	3267.a	1.a	$1$	$6$	$6$	$26.087$	6.6.19783872.1	None	✓	✓			3267.2.a.bc	$2$	$1$	\(0\)	\(0\)	\(-8\)	\(0\)		$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q+\beta _{1}q^{2}+\beta _{2}q^{4}+(-1+\beta _{3})q^{5}+(-\beta _{4}+\cdots)q^{7}+\cdots\)
3267.2.a.bd	$3267$	$2$	3267.a	1.a	$1$	$6$	$6$	$26.087$	6.6.19783872.1	None	✓	✓			3267.2.a.bc	$2$	$0$	\(0\)	\(0\)	\(8\)	\(0\)		$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+\beta _{1}q^{2}+\beta _{2}q^{4}+(1-\beta _{3})q^{5}+(\beta _{4}+\cdots)q^{7}+\cdots\)
3267.2.a.be	$3267$	$2$	3267.a	1.a	$1$	$8$	$8$	$26.087$	\(\mathbb{Q}[x]/(x^{8} - \cdots)\)	None	✓				297.2.f.a	$1$	$1$	\(-4\)	\(0\)	\(-2\)	\(-1\)		$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q+(-1+\beta _{1})q^{2}+(2-\beta _{1}+\beta _{2})q^{4}+\cdots\)
3267.2.a.bf	$3267$	$2$	3267.a	1.a	$1$	$8$	$8$	$26.087$	\(\mathbb{Q}[x]/(x^{8} - \cdots)\)	None	✓				297.2.f.a	$1$	$1$	\(-4\)	\(0\)	\(2\)	\(1\)		$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q+(-1+\beta _{1})q^{2}+(2-\beta _{1}+\beta _{2})q^{4}+\cdots\)
3267.2.a.bg	$3267$	$2$	3267.a	1.a	$1$	$8$	$8$	$26.087$	8.8.\(\cdots\).1	None	✓				297.2.f.c	$2$	$1$	\(0\)	\(0\)	\(0\)	\(-6\)		$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q+\beta _{1}q^{2}+(1+\beta _{2})q^{4}+(-\beta _{1}-\beta _{6}+\cdots)q^{5}+\cdots\)
3267.2.a.bh	$3267$	$2$	3267.a	1.a	$1$	$8$	$8$	$26.087$	8.8.\(\cdots\).1	None	✓				297.2.f.c	$2$	$0$	\(0\)	\(0\)	\(0\)	\(6\)		$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+\beta _{1}q^{2}+(1+\beta _{2})q^{4}+(\beta _{1}+\beta _{6}+\beta _{7})q^{5}+\cdots\)
3267.2.a.bi	$3267$	$2$	3267.a	1.a	$1$	$8$	$8$	$26.087$	8.8.\(\cdots\).1	None	✓				297.2.f.b	$2$	$1$	\(0\)	\(0\)	\(0\)	\(-10\)		$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q+\beta _{1}q^{2}+(1+\beta _{2})q^{4}-\beta _{7}q^{5}+(-1+\cdots)q^{7}+\cdots\)
3267.2.a.bj	$3267$	$2$	3267.a	1.a	$1$	$8$	$8$	$26.087$	8.8.\(\cdots\).1	None	✓				297.2.f.b	$2$	$0$	\(0\)	\(0\)	\(0\)	\(10\)		$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+\beta _{1}q^{2}+(1+\beta _{2})q^{4}+\beta _{7}q^{5}+(1+\beta _{5}+\cdots)q^{7}+\cdots\)
3267.2.a.bk	$3267$	$2$	3267.a	1.a	$1$	$8$	$8$	$26.087$	8.8.\(\cdots\).1	None	✓	✓			3267.2.a.bk	$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)		$-$	$+$	$-$	$2^{3}$	$\mathrm{SU}(2)$	\(q-\beta _{2}q^{2}+(3-\beta _{4})q^{4}+\beta _{6}q^{5}+(-\beta _{1}+\cdots)q^{7}+\cdots\)
3267.2.a.bl	$3267$	$2$	3267.a	1.a	$1$	$8$	$8$	$26.087$	\(\mathbb{Q}[x]/(x^{8} - \cdots)\)	None	✓				297.2.f.a	$1$	$0$	\(4\)	\(0\)	\(-2\)	\(1\)		$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+(1-\beta _{1})q^{2}+(2-\beta _{1}+\beta _{2})q^{4}-\beta _{5}q^{5}+\cdots\)
3267.2.a.bm	$3267$	$2$	3267.a	1.a	$1$	$8$	$8$	$26.087$	\(\mathbb{Q}[x]/(x^{8} - \cdots)\)	None	✓				297.2.f.a	$1$	$0$	\(4\)	\(0\)	\(2\)	\(-1\)		$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+(1-\beta _{1})q^{2}+(2-\beta _{1}+\beta _{2})q^{4}+\beta _{5}q^{5}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_0(3267))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_0(3267)) \simeq \) \(S_{2}^{\mathrm{new}}(\Gamma_0(11))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(27))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(33))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(99))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(121))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(297))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(363))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(1089))\)\(^{\oplus 2}\)