Space of modular forms of level 14 and weight 48

• Label: 14.48
• Level: 14
• Weight: 48
• Dimension: 88
• Nonzero newspaces: 2
• Newform subspaces: 6
• Sturm bound: 576
• Trace bound: 1

Defining parameters

Level:	\( N \)	=	\( 14 = 2 \cdot 7 \)
Weight:	\( k \)	=	\( 48 \)
Nonzero newspaces:			\( 2 \)
Newform subspaces:			\( 6 \)
Sturm bound:			\(576\)
Trace bound:			\(1\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{48}(\Gamma_1(14))\).

	Total	New	Old
Modular forms	288	88	200
Cusp forms	276	88	188
Eisenstein series	12	0	12

Trace form

88 * q + 16777216 * q^2 - 39596886558 * q^3 - 562949953421312 * q^4 - 49360484012877474 * q^5 + 612282630867517440 * q^6 + 87004072083103998880 * q^7 + 1180591620717411303424 * q^8 - 110808050157773034933756 * q^9 - 600110070720122515881984 * q^10 - 5267414137419687003146076 * q^11 - 2786383180431884405440512 * q^12 - 457150041484669427467782934 * q^13 - 447903730676388438525083648 * q^14 + 8646670124848895170867928808 * q^15 - 39614081257132168796771975168 * q^16 + 177846254326634366791195065276 * q^17 + 336583598217788354352107225088 * q^18 - 750813762382778934564784842778 * q^19 - 10500599488022939081061087313920 * q^20 - 76697814147420721525267880783154 * q^21 + 2523331750809654232011585355776 * q^22 + 598961718884796442927574639677608 * q^23 + 153949784061765094142905996541952 * q^24 + 1855511302750103321719143633892780 * q^25 + 2099183835185795094220312628166656 * q^26 + 7411757810780480657572609368111468 * q^27 + 11265523056233007979487475458375680 * q^28 + 92412799717683028896055281790243908 * q^29 + 8417420121892675473493846715793408 * q^30 - 59361703053035039870347212992758084 * q^31 + 83076749736557242056487941267521536 * q^32 + 36283923784724763621308108534901456 * q^33 - 2983276301793238280608757390864547840 * q^34 + 400497629178863573939234168306940450 * q^35 + 51088011597921910191963898923366481920 * q^36 - 22724748461001162114903668607358658812 * q^37 + 43121028301161154622404153861927337984 * q^38 - 75410850862097526526158203424786778512 * q^39 - 42228992044944152573155112969752805376 * q^40 + 303991221756848501980470291367019818932 * q^41 - 154232588011504641988700332047942549504 * q^42 - 2123964187137861575448305458169419373428 * q^43 - 370661317913896640595044688375488446464 * q^44 + 1241523685565523535294428425190459513462 * q^45 - 984035789326207814197442013474613886976 * q^46 + 9149860198311272431986208556806442575140 * q^47 - 196074285204757064532285907165111123968 * q^48 + 30819876329076660847924313931698110303960 * q^49 - 6767827645623488143953916090443792121856 * q^50 - 10208558364941369373413608626718848705540 * q^51 + 29397745677092646457808988496482862628864 * q^52 - 173656036109419802557626215568559662708384 * q^53 + 88954036547893435311773668425609712238592 * q^54 + 299715933054158216423621138635428464875512 * q^55 + 102668186112819312124089559724796053291008 * q^56 - 157295953274157153309554990780538570179148 * q^57 + 727108988334646998093082210701359519367168 * q^58 - 259217116069633467028393022289709012666362 * q^59 + 671824458772454162190478192737799442006016 * q^60 - 2540676380699543710735123513901841230520226 * q^61 - 252458261242394789106112947278786137686016 * q^62 - 2410006029833899849907669995388934030137196 * q^63 + 30663524647979606819611612624891497070723072 * q^64 + 8282707175624457495031700292392987702726484 * q^65 + 10219426116962610679808815127542703245492224 * q^66 - 21190007414141422897925000375764874182239304 * q^67 + 12514817573666703067018875144061013421195264 * q^68 - 95997141872320182810558105185004832840282464 * q^69 + 24129407684072610436317339098501368233590784 * q^70 - 156525157236169868794856694645573624304616712 * q^71 + 23684965117385193347349869370380627510034432 * q^72 + 118411992175284372657785512510202757045704984 * q^73 - 110646525376420201297552731650238825002696704 * q^74 + 1437057199315352285789331841229249001642134454 * q^75 - 576427637793346726619290914236023620335828992 * q^76 + 1485734128858171374903059814424584468760000956 * q^77 - 907567105638315006873653714499507224850726912 * q^78 + 301214412558602587499470995576625500829226744 * q^79 - 244421278072187700650121143771562963269320704 * q^80 - 1874881480005583583056322605187384335421640804 * q^81 + 1286434968618833742693717050960254922196516864 * q^82 + 1471827116338371017769324686715596184073535070 * q^83 + 2192623694641778201574842114702972482549186560 * q^84 - 2502805563769514123661145416790374612591451620 * q^85 - 5336728463964874565621453225944841981916086272 * q^86 + 19080894778195452263806308257122275443481421524 * q^87 - 2512845133051897864853481791498259283958562816 * q^88 + 6375261790600219424309222231918732335061529264 * q^89 - 57451742562771323686449623529086728943532244992 * q^90 + 70265314785220253208486780381495173546925119894 * q^91 - 856753799521890017505861663158738972886171648 * q^92 - 91282998359210733409186101856625352096258964680 * q^93 + 61273435100871911553701772137850708379406696448 * q^94 - 107556883332585107354939012953257128935414585848 * q^95 + 10833252970848962533427485172530756517917360128 * q^96 + 9661666407326560774837257786668512629057859484 * q^97 + 26951773563030474254994162730458141695257083904 * q^98 - 366385289109014085812703016058674414757831372268 * q^99

Decomposition of \(S_{48}^{\mathrm{new}}(\Gamma_1(14))\)

We only show spaces with even 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
14.48.a	\(\chi_{14}(1, \cdot)\)	14.48.a.a	5	1
		14.48.a.b	6
		14.48.a.c	6
		14.48.a.d	7
14.48.c	\(\chi_{14}(9, \cdot)\)	14.48.c.a	32	2
		14.48.c.b	32

Decomposition of \(S_{48}^{\mathrm{old}}(\Gamma_1(14))\) into lower level spaces

\( S_{48}^{\mathrm{old}}(\Gamma_1(14)) \cong \) \(S_{48}^{\mathrm{new}}(\Gamma_1(1))\)\(^{\oplus 4}\)\(\oplus\)\(S_{48}^{\mathrm{new}}(\Gamma_1(2))\)\(^{\oplus 2}\)\(\oplus\)\(S_{48}^{\mathrm{new}}(\Gamma_1(7))\)\(^{\oplus 2}\)