Space of modular forms of level 12 and weight 18

• Label: 12.18
• Level: 12
• Weight: 18
• Dimension: 34
• Nonzero newspaces: 2
• Newform subspaces: 3
• Sturm bound: 144
• Trace bound: 1

Defining parameters

Level:	\( N \)	=	\( 12 = 2^{2} \cdot 3 \)
Weight:	\( k \)	=	\( 18 \)
Nonzero newspaces:			\( 2 \)
Newform subspaces:			\( 3 \)
Sturm bound:			\(144\)
Trace bound:			\(1\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{18}(\Gamma_1(12))\).

	Total	New	Old
Modular forms	73	38	35
Cusp forms	63	34	29
Eisenstein series	10	4	6

Trace form

34 * q - 54808 * q^4 - 1477980 * q^5 - 4960776 * q^6 - 24263960 * q^7 + 165968418 * q^9 + 46839088 * q^10 - 1032380208 * q^11 + 2598308520 * q^12 - 652740340 * q^13 + 11415352680 * q^15 - 41721285088 * q^16 + 43735163220 * q^17 + 27568791600 * q^18 - 153568558640 * q^19 + 92741616744 * q^21 - 493958165040 * q^22 - 80527437360 * q^23 - 253565784288 * q^24 - 1983764722498 * q^25 - 2695436033040 * q^28 - 2282551050492 * q^29 - 2169979068432 * q^30 + 2168009129608 * q^31 - 21965600274360 * q^33 + 6944208632512 * q^34 + 13207404535920 * q^35 - 12909384040056 * q^36 - 46787236254100 * q^37 + 28716563238480 * q^39 + 21066454663744 * q^40 + 17740604240100 * q^41 + 55835180334480 * q^42 + 97730802970480 * q^43 + 90391071100836 * q^45 + 235918828815264 * q^46 - 172678557920400 * q^47 + 299462725247520 * q^48 - 404742697237870 * q^49 - 287565080446512 * q^51 + 544732086739120 * q^52 + 1087043089943700 * q^53 + 487051858173384 * q^54 + 190011694259520 * q^55 - 1891784499679080 * q^57 + 230877304263760 * q^58 - 182503267515072 * q^59 - 345098683994304 * q^60 - 7893665904338692 * q^61 - 1044483916475160 * q^63 + 1003775054518400 * q^64 + 4453501300162200 * q^65 - 2371521654206832 * q^66 - 669199133977280 * q^67 - 3453734292265632 * q^69 - 949041839387232 * q^70 + 12010628577638160 * q^71 + 5817303713532480 * q^72 - 6197649738579820 * q^73 - 16871662953986400 * q^75 - 2051936325547056 * q^76 + 14312669809183200 * q^77 + 22261766802491280 * q^78 - 12372197413768664 * q^79 + 31727349360455202 * q^81 + 7596239161270240 * q^82 + 43379661699213840 * q^83 - 8356700998055568 * q^84 - 10538064781908184 * q^85 - 33328475346849480 * q^87 - 18469777603302720 * q^88 + 98415339645711060 * q^89 - 68814047068261392 * q^90 - 1278589146387280 * q^91 - 80169926343741960 * q^93 - 61915224567506112 * q^94 + 147953880687427200 * q^95 - 45410293501908864 * q^96 - 879948917195740 * q^97 - 44440582779697968 * q^99

Decomposition of \(S_{18}^{\mathrm{new}}(\Gamma_1(12))\)

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
12.18.a	\(\chi_{12}(1, \cdot)\)	12.18.a.a	1	1
		12.18.a.b	1
12.18.b	\(\chi_{12}(11, \cdot)\)	12.18.b.a	32	1

Decomposition of \(S_{18}^{\mathrm{old}}(\Gamma_1(12))\) into lower level spaces

\( S_{18}^{\mathrm{old}}(\Gamma_1(12)) \cong \) \(S_{18}^{\mathrm{new}}(\Gamma_1(1))\)\(^{\oplus 6}\)\(\oplus\)\(S_{18}^{\mathrm{new}}(\Gamma_1(2))\)\(^{\oplus 4}\)\(\oplus\)\(S_{18}^{\mathrm{new}}(\Gamma_1(3))\)\(^{\oplus 3}\)\(\oplus\)\(S_{18}^{\mathrm{new}}(\Gamma_1(4))\)\(^{\oplus 2}\)\(\oplus\)\(S_{18}^{\mathrm{new}}(\Gamma_1(6))\)\(^{\oplus 2}\)