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

• Label: 150.12.e
• Level: $150$
• Weight: $12$
• Character orbit: 150.e
• Rep. character: $\chi_{150}(107,\cdot)$
• Character field: $\Q(\zeta_{4})$
• Dimension: $132$
• Sturm bound: $360$

Defining parameters

Level:	\( N \)	\(=\)	\( 150 = 2 \cdot 3 \cdot 5^{2} \)
Weight:	\( k \)	\(=\)	\( 12 \)
Character orbit:	\([\chi]\)	\(=\)	150.e (of order \(4\) and degree \(2\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 15 \)
Character field:			\(\Q(i)\)
Sturm bound:			\(360\)

Dimensions

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

	Total	New	Old
Modular forms	684	132	552
Cusp forms	636	132	504
Eisenstein series	48	0	48

Trace form

132 * q + 1012 * q^3 + 5888 * q^6 + 31508 * q^7 - 1036288 * q^12 - 3387840 * q^13 - 138412032 * q^16 + 10875136 * q^18 - 33274576 * q^21 + 39398528 * q^22 + 57593668 * q^27 + 32264192 * q^28 - 79751064 * q^31 - 767958788 * q^33 + 151052288 * q^36 + 1930138392 * q^37 - 1300763008 * q^42 + 3260565768 * q^43 - 3804823552 * q^46 - 1061158912 * q^48 + 3317168116 * q^51 + 3469148160 * q^52 - 12569857328 * q^57 + 31479955840 * q^58 - 53579567032 * q^61 - 60823552988 * q^63 - 22599212416 * q^66 + 50272721552 * q^67 - 11136139264 * q^72 + 69851190940 * q^73 - 6155558912 * q^76 - 56643605760 * q^78 + 131183478304 * q^81 - 20509608448 * q^82 + 181212446620 * q^87 + 40344092672 * q^88 + 315302592000 * q^91 - 164686825064 * q^93 - 6174015488 * q^96 - 360271956804 * 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

\( S_{12}^{\mathrm{old}}(150, [\chi]) \simeq \) \(S_{12}^{\mathrm{new}}(15, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{12}^{\mathrm{new}}(30, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{12}^{\mathrm{new}}(75, [\chi])\)\(^{\oplus 2}\)