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

• Label: 150.12.l
• Level: $150$
• Weight: $12$
• Character orbit: 150.l
• Rep. character: $\chi_{150}(17,\cdot)$
• Character field: $\Q(\zeta_{20})$
• Dimension: $880$
• Sturm bound: $360$

Defining parameters

Level:	\( N \)	\(=\)	\( 150 = 2 \cdot 3 \cdot 5^{2} \)
Weight:	\( k \)	\(=\)	\( 12 \)
Character orbit:	\([\chi]\)	\(=\)	150.l (of order \(20\) and degree \(8\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 75 \)
Character field:			\(\Q(\zeta_{20})\)
Sturm bound:			\(360\)

Dimensions

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

	Total	New	Old
Modular forms	2672	880	1792
Cusp forms	2608	880	1728
Eisenstein series	64	0	64

Trace form

880 * q + 1012 * q^3 + 31508 * q^7 + 163456 * q^10 - 1036288 * q^12 - 3387840 * q^13 - 2029928 * q^15 + 230686720 * q^16 + 10875136 * q^18 + 109603960 * q^19 - 110861952 * q^22 + 410102696 * q^25 + 57593668 * q^27 - 129056768 * q^28 + 177036672 * q^30 - 767958788 * q^33 + 1173256960 * q^34 + 1930138392 * q^37 - 4251492040 * q^39 - 796131328 * q^40 - 1300763008 * q^42 + 3260565768 * q^43 - 8045383512 * q^45 - 1061158912 * q^48 + 3469148160 * q^52 - 30846414972 * q^55 + 43622590112 * q^57 + 31479955840 * q^58 - 22502055936 * q^60 + 78208204192 * q^63 + 32686199712 * q^67 + 224018151140 * q^69 + 97302951296 * q^70 - 11136139264 * q^72 - 62994010420 * q^73 - 268151678268 * q^75 + 183082119040 * q^78 + 256517168080 * q^79 - 47436356440 * q^81 - 124613157888 * q^82 - 298788925440 * q^84 - 711129114848 * q^85 + 589143528320 * q^87 + 40344092672 * q^88 - 71900759168 * q^90 + 600734471796 * q^93 - 284871120544 * q^97

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

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