Space of modular forms of level 3 and weight 37

• Label: 3.37
• Level: 3
• Weight: 37
• Dimension: 11
• Nonzero newspaces: 1
• Newform subspaces: 2
• Sturm bound: 24
• Trace bound: 0

Defining parameters

Level:	\( N \)	=	\( 3 \)
Weight:	\( k \)	=	\( 37 \)
Nonzero newspaces:			\( 1 \)
Newform subspaces:			\( 2 \)
Sturm bound:			\(24\)
Trace bound:			\(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{37}(\Gamma_1(3))\).

	Total	New	Old
Modular forms	13	13	0
Cusp forms	11	11	0
Eisenstein series	2	2	0

Trace form

11 * q - 164736261 * q^3 - 366480813328 * q^4 + 77238909590832 * q^6 + 1529656139588998 * q^7 + 219422675471657499 * q^9 + 976353968400999840 * q^10 + 12713663984972326704 * q^12 - 26664183895525067642 * q^13 + 7346306914204243680 * q^15 + 12912742276961748775040 * q^16 - 116380061882656121268000 * q^18 + 138821577295896839366518 * q^19 - 2247956081834234679653850 * q^21 + 6375713195756021276887200 * q^22 - 18479722715707703137259904 * q^24 + 7279508127194401821131675 * q^25 + 95231216966669978862527019 * q^27 - 391577988767589793638714272 * q^28 + 832077359475776822335514400 * q^30 - 1733608557857573255379602138 * q^31 - 1833168501223628340439879200 * q^33 + 11044532239488942328340194176 * q^34 - 21948402658393775440817520912 * q^36 + 12786450877411433164392216358 * q^37 - 9936827303902532409454966170 * q^39 + 14850499435375431475622142720 * q^40 + 551003488989169331884355647200 * q^42 - 515487319179727929010406869802 * q^43 - 75992211973807694886478996800 * q^45 - 887182867438274648036289139776 * q^46 - 4346257047411219928317289501056 * q^48 + 9110404204240350847814031518529 * q^49 - 2349347159740543712848217109888 * q^51 - 13203626071464804773830678836512 * q^52 + 35390782846752825865826083751568 * q^54 - 30568574550133842572339360395200 * q^55 + 96963716675033228271210975522198 * q^57 - 112605799975805654976196455444000 * q^58 + 19469866547367779716225803605760 * q^60 + 66999347224237022458014520403782 * q^61 - 20218845986102637586445162314842 * q^63 - 304236018528391125615295992251392 * q^64 + 1808913396822349027193824888380960 * q^66 - 3004194906649294236056896403510282 * q^67 + 5226032060124551681525948207907648 * q^69 - 11529100185846942980259125797809600 * q^70 + 19879821238248816464160255047788800 * q^72 - 10390545366461872145216469125969162 * q^73 + 21376990929305061495027761443252875 * q^75 - 39862084315848733842646101136440224 * q^76 + 66756441224105756984056960627624800 * q^78 - 71385979381146382550075928433902362 * q^79 + 124901631937240804827635146103482731 * q^81 - 295731520386077266321378186874491200 * q^82 + 565465498335095720662452392509252320 * q^84 - 416995278796335191384264774379644160 * q^85 + 502161755301600073278417594406864800 * q^87 - 1043368725545479380062123692743456000 * q^88 + 1148239664725140620121403824942828960 * q^90 - 676075249402808126607982688855079700 * q^91 + 1136822552118204808049516782296691398 * q^93 - 1775468098694354855547362712124166784 * q^94 + 2402404280227868861578148783194622976 * q^96 - 1638469121614694224091416117067972522 * q^97 + 2995711137935834844910948248309577920 * q^99

Decomposition of \(S_{37}^{\mathrm{new}}(\Gamma_1(3))\)

We only show spaces with odd parity, since no modular forms exist when this condition is not satisfied. Within each space \( S_k^{\mathrm{new}}(N, \chi) \) we list available newforms together with their dimension.

Label	\(\chi\)	Newforms	Dimension	\(\chi\) degree
3.37.b	\(\chi_{3}(2, \cdot)\)	3.37.b.a	1	1
		3.37.b.b	10