Space of modular forms of level 9, weight 14, and trivial character

• Label: 9.14.a
• Level: $9$
• Weight: $14$
• Character orbit: 9.a
• Rep. character: $\chi_{9}(1,\cdot)$
• Character field: $\Q$
• Dimension: $5$
• Newform subspaces: $3$
• Sturm bound: $14$
• Trace bound: $2$

Defining parameters

Level:	\( N \)	\(=\)	\( 9 = 3^{2} \)
Weight:	\( k \)	\(=\)	\( 14 \)
Character orbit:	\([\chi]\)	\(=\)	9.a (trivial)
Character field:			\(\Q\)
Newform subspaces:			\( 3 \)
Sturm bound:			\(14\)
Trace bound:			\(2\)
Distinguishing \(T_p\):			\(2\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{14}(\Gamma_0(9))\).

	Total	New	Old
Modular forms	15	6	9
Cusp forms	11	5	6
Eisenstein series	4	1	3

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

\(3\)	Dim
\(+\)	\(2\)
\(-\)	\(3\)

Trace form

5 * q + 66 * q^2 + 11924 * q^4 - 10506 * q^5 - 52520 * q^7 + 1830552 * q^8 - 4437036 * q^10 + 10510500 * q^11 - 35372882 * q^13 + 124741392 * q^14 - 54505456 * q^16 + 33656058 * q^17 + 205818292 * q^19 - 415819704 * q^20 + 250515144 * q^22 - 1690137480 * q^23 + 501842531 * q^25 - 2614700676 * q^26 + 4579354720 * q^28 + 5980875582 * q^29 - 12934541360 * q^31 + 9664679520 * q^32 - 8546623524 * q^34 + 23208096000 * q^35 - 1474210610 * q^37 - 22841047416 * q^38 + 38582099568 * q^40 - 10580286414 * q^41 + 14412634924 * q^43 - 166960484592 * q^44 + 29387957904 * q^46 + 98563919232 * q^47 + 29896743453 * q^49 - 216267297954 * q^50 - 40326577448 * q^52 + 430461936630 * q^53 - 559157161464 * q^55 + 364557046080 * q^56 + 539066189412 * q^58 + 957730645284 * q^59 - 625553765114 * q^61 - 1329517977600 * q^62 + 561594758720 * q^64 - 521388486348 * q^65 + 949107615172 * q^67 - 1665976898088 * q^68 - 923199873120 * q^70 - 529876859256 * q^71 + 1361394217450 * q^73 + 1288521504492 * q^74 + 2838948960400 * q^76 - 1847993854080 * q^77 - 5590913757728 * q^79 + 4705679741856 * q^80 - 4872625014420 * q^82 + 3450268778268 * q^83 + 10932244963092 * q^85 + 10824101299320 * q^86 - 19552441388832 * q^88 - 5505789611214 * q^89 - 1172721458896 * q^91 - 9209631335520 * q^92 + 39984159883680 * q^94 - 15165024536184 * q^95 - 12892359050078 * q^97 + 3130819722738 * q^98

Decomposition of \(S_{14}^{\mathrm{new}}(\Gamma_0(9))\) 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
9.14.a.a	$9$	$14$	9.a	1.a	$1$	$1$	$1$	$9.651$	\(\Q\)	None	✓				3.14.a.a	$1$	$0$	\(12\)	\(0\)	\(30210\)	\(235088\)		$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+12q^{2}-8048q^{4}+30210q^{5}+235088q^{7}+\cdots\)
9.14.a.b	$9$	$14$	9.a	1.a	$1$	$2$	$2$	$9.651$	\(\Q(\sqrt{55}) \)	None	✓	✓	✓	✓	9.14.a.b	$2$	$1$	\(0\)	\(0\)	\(0\)	\(-266600\)		$+$	$+$	$2^{2}\cdot 3$	$\mathrm{SU}(2)$	\(q+\beta q^{2}-272q^{4}-520\beta q^{5}-133300q^{7}+\cdots\)
9.14.a.c	$9$	$14$	9.a	1.a	$1$	$2$	$2$	$9.651$	\(\Q(\sqrt{1969}) \)	None	✓		✓		3.14.a.b	$1$	$0$	\(54\)	\(0\)	\(-40716\)	\(-21008\)		$-$	$-$	$2\cdot 3$	$\mathrm{SU}(2)$	\(q+(3^{3}-\beta )q^{2}+(10258-54\beta )q^{4}+(-20358+\cdots)q^{5}+\cdots\)

Decomposition of \(S_{14}^{\mathrm{old}}(\Gamma_0(9))\) into lower level spaces

\( S_{14}^{\mathrm{old}}(\Gamma_0(9)) \simeq \) \(S_{14}^{\mathrm{new}}(\Gamma_0(3))\)\(^{\oplus 2}\)