Space of modular forms of level 14, weight 42, and trivial character

• Label: 14.42.a
• Level: $14$
• Weight: $42$
• Character orbit: 14.a
• Rep. character: $\chi_{14}(1,\cdot)$
• Character field: $\Q$
• Dimension: $20$
• Newform subspaces: $4$
• Sturm bound: $84$
• Trace bound: $2$

Defining parameters

Level:	\( N \)	\(=\)	\( 14 = 2 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 42 \)
Character orbit:	\([\chi]\)	\(=\)	14.a (trivial)
Character field:			\(\Q\)
Newform subspaces:			\( 4 \)
Sturm bound:			\(84\)
Trace bound:			\(2\)
Distinguishing \(T_p\):			\(3\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{42}(\Gamma_0(14))\).

	Total	New	Old
Modular forms	84	20	64
Cusp forms	80	20	60
Eisenstein series	4	0	4

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

\(2\)	\(7\)	Fricke		Total				Cusp				Eisenstein
				All	New	Old		All	New	Old		All	New	Old
\(+\)	\(+\)	\(+\)		\(20\)	\(5\)	\(15\)		\(19\)	\(5\)	\(14\)		\(1\)	\(0\)	\(1\)
\(+\)	\(-\)	\(-\)		\(22\)	\(6\)	\(16\)		\(21\)	\(6\)	\(15\)		\(1\)	\(0\)	\(1\)
\(-\)	\(+\)	\(-\)		\(21\)	\(5\)	\(16\)		\(20\)	\(5\)	\(15\)		\(1\)	\(0\)	\(1\)
\(-\)	\(-\)	\(+\)		\(21\)	\(4\)	\(17\)		\(20\)	\(4\)	\(16\)		\(1\)	\(0\)	\(1\)
Plus space		\(+\)		\(41\)	\(9\)	\(32\)		\(39\)	\(9\)	\(30\)		\(2\)	\(0\)	\(2\)
Minus space		\(-\)		\(43\)	\(11\)	\(32\)		\(41\)	\(11\)	\(30\)		\(2\)	\(0\)	\(2\)

Trace form

20 * q - 2097152 * q^2 - 20840159286 * q^3 + 21990232555520 * q^4 - 292600339624086 * q^5 - 1288700174532608 * q^6 - 2305843009213693952 * q^8 + 251594660431719250472 * q^9 - 612418167101997449216 * q^10 - 4609165549129692062940 * q^11 - 22913997459660981927936 * q^12 - 184281298210714784133778 * q^13 - 167336510850569603121152 * q^14 + 7832285068393832356597160 * q^15 + 24178516392292583494123520 * q^16 + 13705203927437231007126828 * q^17 - 193655894294902640952213504 * q^18 - 92273224721193560242263938 * q^19 - 321717475707889229796212736 * q^20 + 261490270702960651851946034 * q^21 - 2351562021662431027985907712 * q^22 + 8771497200659116248129869256 * q^23 - 1416940826615563122070519808 * q^24 + 33498759771506445319061102616 * q^25 - 15356380419067162729205727232 * q^26 - 81763022290874150819241171396 * q^27 + 89028613227791471346497370756 * q^29 - 1972271108093743773747679068160 * q^30 - 8670331367441744840091575266564 * q^31 - 2535301200456458802993406410752 * q^32 - 27080045378051284782515050107728 * q^33 + 7102368887128686493506845278208 * q^34 - 40909937083464565069435516665414 * q^35 + 276631254631029611988703376310272 * q^36 - 396341417166437455283978397514076 * q^37 + 256920401088622413668762871922688 * q^38 - 739067994950002589900089223658544 * q^39 - 673360895789911588008484055023616 * q^40 + 3579002208856533371659034973579252 * q^41 - 583466335751533334127593706749952 * q^42 + 7976597015931233860903415724765004 * q^43 - 5067831115612648620256786844221440 * q^44 + 29658511706402119672722437493915298 * q^45 - 26753921142111813907093025506459648 * q^46 + 21832353817828167940886407711955940 * q^47 - 25194206645726975136699430087950336 * q^48 + 127336115218180559714828702784480020 * q^49 - 92547385086907776611216128489816064 * q^50 + 230104335623764837283194023522511180 * q^51 - 202619430164337488547398706924617728 * q^52 + 443984188702624820340543743898407112 * q^53 - 1198354877262577140634543379865141248 * q^54 + 1058320457399698246166233788942457016 * q^55 - 183988439431666070624524125656317952 * q^56 - 2012173240098410371793689826765302404 * q^57 + 260342863245199805247921920269090816 * q^58 - 1546544969855717231580207708386783442 * q^59 + 8611688504755362104241001483898716160 * q^60 - 7285740802095054040793043389337533734 * q^61 + 20108100268370704849531216442962214912 * q^62 - 16455841522330375504637758940527469772 * q^63 + 26584559915698317458076141205606891520 * q^64 - 30163232026395728294848003766397087924 * q^65 + 36121276561989034002887694264756600832 * q^66 - 25753243171487848828514862133371762552 * q^67 + 15069031079258538052712158511159574528 * q^68 + 179011184937374024981104977810225830368 * q^69 + 41113686297370082924934515426764783616 * q^70 - 137832419904050301875462940887533370952 * q^71 - 212926907564605394532809548413328687104 * q^72 - 127966175963012901389170017555335704512 * q^73 - 108564803331807340722438721749177597952 * q^74 - 628583875672134599103600481035786532930 * q^75 - 101455483513340175187540339381803941888 * q^76 - 7882822620109079825735957070820779612 * q^77 - 818743603594638762499465913473395851264 * q^78 + 498929566609565755167984236209055345048 * q^79 - 353732105399567024938332786119342555136 * q^80 + 4050926011006641484398031957065411627008 * q^81 + 1091365977333897156869492014828216123392 * q^82 - 5846413793931433751686525558367013886410 * q^83 + 287511593188199150100211212796647440384 * q^84 + 8042033822608288719082331993605383760628 * q^85 + 1117608301749115817719228944773996871680 * q^86 - 10194608483047451899414988738015292357388 * q^87 - 2585569786254280913166114399210031808512 * q^88 + 6504299216937231267204474119027329005768 * q^89 - 8087661242826945063914025338091069243392 * q^90 + 21985786807268445164355373301270016306350 * q^91 + 9644363165129332206074882461510618054656 * q^92 + 31149782909115516841235195299345437213800 * q^93 + 12975924854168803262196232273787967504384 * q^94 - 84611377680858686759637082369427228045880 * q^95 - 1557942914734348793322633825556530987008 * q^96 + 33685897863269996514451594043135025241932 * q^97 - 13352159435101889858353622185093892145152 * q^98 - 46094270864109596552562647710083059191276 * q^99

Decomposition of \(S_{42}^{\mathrm{new}}(\Gamma_0(14))\) 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	7
14.42.a.a	$14$	$42$	14.a	1.a	$1$	$4$	$4$	$149.060$	\(\mathbb{Q}[x]/(x^{4} - \cdots)\)	None	✓	✓	✓	✓	14.42.a.a	$1$	$1$	\(4194304\)	\(-6441397578\)	\(-22\!\cdots\!50\)	\(31\!\cdots\!04\)		$-$	$-$	$+$	$2^{12}\cdot 3^{6}\cdot 5^{2}\cdot 7^{2}$	$\mathrm{SU}(2)$	\(q+2^{20}q^{2}+(-1610349395-\beta _{1}+\cdots)q^{3}+\cdots\)
14.42.a.b	$14$	$42$	14.a	1.a	$1$	$5$	$5$	$149.060$	\(\mathbb{Q}[x]/(x^{5} - \cdots)\)	None	✓	✓	✓	✓	14.42.a.b	$1$	$1$	\(-5242880\)	\(-7465466466\)	\(32\!\cdots\!40\)	\(-39\!\cdots\!05\)		$+$	$+$	$+$	$2^{22}\cdot 3^{10}\cdot 5^{3}\cdot 7^{4}$	$\mathrm{SU}(2)$	\(q-2^{20}q^{2}+(-1493093293-\beta _{1}+\cdots)q^{3}+\cdots\)
14.42.a.c	$14$	$42$	14.a	1.a	$1$	$5$	$5$	$149.060$	\(\mathbb{Q}[x]/(x^{5} - \cdots)\)	None	✓	✓	✓	✓	14.42.a.c	$1$	$0$	\(5242880\)	\(-4593182194\)	\(-21\!\cdots\!76\)	\(-39\!\cdots\!05\)		$-$	$+$	$-$	$2^{22}\cdot 3^{6}\cdot 5^{2}\cdot 7^{4}$	$\mathrm{SU}(2)$	\(q+2^{20}q^{2}+(-918636439-\beta _{1})q^{3}+\cdots\)
14.42.a.d	$14$	$42$	14.a	1.a	$1$	$6$	$6$	$149.060$	\(\mathbb{Q}[x]/(x^{6} - \cdots)\)	None	✓	✓	✓	✓	14.42.a.d	$1$	$0$	\(-6291456\)	\(-2340113048\)	\(-17\!\cdots\!00\)	\(47\!\cdots\!06\)		$+$	$-$	$-$	$2^{30}\cdot 3^{10}\cdot 5^{3}\cdot 7^{6}$	$\mathrm{SU}(2)$	\(q-2^{20}q^{2}+(-390018841+\beta _{1})q^{3}+\cdots\)

Decomposition of \(S_{42}^{\mathrm{old}}(\Gamma_0(14))\) into lower level spaces

\( S_{42}^{\mathrm{old}}(\Gamma_0(14)) \simeq \) \(S_{42}^{\mathrm{new}}(\Gamma_0(1))\)\(^{\oplus 4}\)\(\oplus\)\(S_{42}^{\mathrm{new}}(\Gamma_0(2))\)\(^{\oplus 2}\)\(\oplus\)\(S_{42}^{\mathrm{new}}(\Gamma_0(7))\)\(^{\oplus 2}\)