Space of modular forms of level 150, weight 12, and Character 150.h

• Label: 150.12.h
• Level: $150$
• Weight: $12$
• Character orbit: 150.h
• Rep. character: $\chi_{150}(19,\cdot)$
• Character field: $\Q(\zeta_{10})$
• Dimension: $216$
• Sturm bound: $360$

Defining parameters

Level:	\( N \)	\(=\)	\( 150 = 2 \cdot 3 \cdot 5^{2} \)
Weight:	\( k \)	\(=\)	\( 12 \)
Character orbit:	\([\chi]\)	\(=\)	150.h (of order \(10\) and degree \(4\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 25 \)
Character field:			\(\Q(\zeta_{10})\)
Sturm bound:			\(360\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{12}(150, [\chi])\).

	Total	New	Old
Modular forms	1336	216	1120
Cusp forms	1304	216	1088
Eisenstein series	32	0	32

Trace form

216 * q + 55296 * q^4 + 4976 * q^5 + 15552 * q^6 + 3188646 * q^9 - 301376 * q^10 + 2939388 * q^11 + 1186326 * q^15 - 56623104 * q^16 + 8389460 * q^17 + 22976792 * q^19 - 31453184 * q^20 + 16336404 * q^21 - 75130240 * q^22 + 103233740 * q^23 + 63700992 * q^24 - 54430346 * q^25 - 31493888 * q^26 - 80660480 * q^28 + 106412888 * q^29 + 462703104 * q^30 - 373185906 * q^31 - 1119457260 * q^33 - 1025164160 * q^34 + 1744391976 * q^35 - 3265173504 * q^36 - 1960058100 * q^37 + 308609024 * q^40 + 382069276 * q^41 - 3115298880 * q^42 + 2006622208 * q^44 - 293827824 * q^45 + 5135156096 * q^46 - 365849480 * q^47 - 49163614804 * q^49 + 7711429376 * q^50 - 5520404016 * q^51 + 6633564300 * q^53 - 918330048 * q^54 + 8093020700 * q^55 + 17165628000 * q^59 + 10447958016 * q^60 + 42086534508 * q^61 - 9376183680 * q^62 - 22654739340 * q^63 + 57982058496 * q^64 - 28753961808 * q^65 + 10018660608 * q^66 + 8793260920 * q^67 - 41173309584 * q^69 - 58608591296 * q^70 - 100547521192 * q^71 + 139465708800 * q^73 - 61725615872 * q^74 - 13087453176 * q^75 - 18121515008 * q^76 + 46765141360 * q^77 - 96024168404 * q^79 + 5217714176 * q^80 - 188286357654 * q^81 - 77230557880 * q^83 - 16728477696 * q^84 + 68348641796 * q^85 + 134031508224 * q^86 + 21724107660 * q^87 - 23926865920 * q^88 + 134181937656 * q^89 + 17795951424 * q^90 + 181868513412 * q^91 - 247394183168 * q^94 - 567229332384 * q^95 + 16307453952 * q^96 + 95484769750 * q^97 + 456740554240 * q^98 + 115711948008 * q^99

Decomposition of \(S_{12}^{\mathrm{new}}(150, [\chi])\) into newform subspaces

The newforms in this space have not yet been added to the LMFDB.

Decomposition of \(S_{12}^{\mathrm{old}}(150, [\chi])\) into lower level spaces

\( S_{12}^{\mathrm{old}}(150, [\chi]) \simeq \) \(S_{12}^{\mathrm{new}}(25, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{12}^{\mathrm{new}}(50, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{12}^{\mathrm{new}}(75, [\chi])\)\(^{\oplus 2}\)