Space of modular forms of level 3, weight 14, and trivial character

• Label: 3.14.a
• Level: $3$
• Weight: $14$
• Character orbit: 3.a
• Rep. character: $\chi_{3}(1,\cdot)$
• Character field: $\Q$
• Dimension: $3$
• Newform subspaces: $2$
• Sturm bound: $4$
• Trace bound: $1$

Defining parameters

Level:	\( N \)	\(=\)	\( 3 \)
Weight:	\( k \)	\(=\)	\( 14 \)
Character orbit:	\([\chi]\)	\(=\)	3.a (trivial)
Character field:			\(\Q\)
Newform subspaces:			\( 2 \)
Sturm bound:			\(4\)
Trace bound:			\(1\)
Distinguishing \(T_p\):			\(2\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{14}(\Gamma_0(3))\).

	Total	New	Old
Modular forms	5	3	2
Cusp forms	3	3	0
Eisenstein series	2	0	2

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
\(+\)	\(1\)
\(-\)	\(2\)

Trace form

3 * q - 66 * q^2 + 729 * q^3 + 12468 * q^4 + 10506 * q^5 - 30618 * q^6 + 214080 * q^7 - 1830552 * q^8 + 1594323 * q^9 + 3799764 * q^10 - 10510500 * q^11 + 20823156 * q^12 + 25582218 * q^13 - 124741392 * q^14 + 51705054 * q^15 + 75107856 * q^16 - 33656058 * q^17 - 35075106 * q^18 + 42232164 * q^19 + 415819704 * q^20 - 186693984 * q^21 - 1181420856 * q^22 + 1690137480 * q^23 - 1618607448 * q^24 - 1339887219 * q^25 + 2614700676 * q^26 + 387420489 * q^27 + 4506839520 * q^28 - 5980875582 * q^29 + 2241473796 * q^30 + 176798904 * q^31 - 9664679520 * q^32 + 8642525364 * q^33 + 1732142556 * q^34 - 23208096000 * q^35 + 6626006388 * q^36 + 21913002690 * q^37 + 22841047416 * q^38 + 6913099710 * q^39 - 31134175632 * q^40 + 10580286414 * q^41 - 86823375120 * q^42 - 4199485476 * q^43 + 166960484592 * q^44 + 5583319146 * q^45 - 164218913136 * q^46 - 98563919232 * q^47 - 37961549424 * q^48 + 188136984267 * q^49 + 216267297954 * q^50 + 146771892594 * q^51 - 56906364648 * q^52 - 430461936630 * q^53 - 16271660538 * q^54 + 185449558536 * q^55 - 364557046080 * q^56 + 342888739596 * q^57 + 359196653412 * q^58 - 957730645284 * q^59 - 51351092424 * q^60 + 45003454602 * q^61 + 1329517977600 * q^62 + 113770889280 * q^63 - 571959536064 * q^64 + 521388486348 * q^65 - 1056911962392 * q^66 - 349796259228 * q^67 + 1665976898088 * q^68 + 21160239768 * q^69 - 2021165313120 * q^70 + 529876859256 * q^71 - 972830385432 * q^72 + 678524322750 * q^73 - 1288521504492 * q^74 - 527627724201 * q^75 + 2883444387216 * q^76 + 1847993854080 * q^77 + 2046952839348 * q^78 - 1786446129720 * q^79 - 4705679741856 * q^80 + 847288609443 * q^81 + 3119523017580 * q^82 - 3450268778268 * q^83 + 6044004840672 * q^84 + 5587286601492 * q^85 - 10824101299320 * q^86 - 2534058734778 * q^87 - 7432535084832 * q^88 + 5505789611214 * q^89 + 2019350379924 * q^90 - 9298036288896 * q^91 + 9209631335520 * q^92 - 8851446703800 * q^93 + 26697141090720 * q^94 + 15165024536184 * q^95 - 3605335005024 * q^96 - 24090183321978 * q^97 - 3130819722738 * q^98 - 5585710630500 * q^99

Decomposition of \(S_{14}^{\mathrm{new}}(\Gamma_0(3))\) 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
3.14.a.a	$3$	$14$	3.a	1.a	$1$	$1$	$1$	$3.217$	\(\Q\)	None	✓	✓	✓	✓	3.14.a.a	$1$	$1$	\(-12\)	\(-729\)	\(-30210\)	\(235088\)		$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q-12q^{2}-3^{6}q^{3}-8048q^{4}-30210q^{5}+\cdots\)
3.14.a.b	$3$	$14$	3.a	1.a	$1$	$2$	$2$	$3.217$	\(\Q(\sqrt{1969}) \)	None	✓	✓	✓	✓	3.14.a.b	$1$	$0$	\(-54\)	\(1458\)	\(40716\)	\(-21008\)		$-$	$-$	$2\cdot 3$	$\mathrm{SU}(2)$	\(q+(-3^{3}-\beta )q^{2}+3^{6}q^{3}+(10258+54\beta )q^{4}+\cdots\)