Space of modular forms of level 912, weight 6, and Character 912.cs

• Label: 912.6.cs
• Level: $912$
• Weight: $6$
• Character orbit: 912.cs
• Rep. character: $\chi_{912}(29,\cdot)$
• Character field: $\Q(\zeta_{36})$
• Dimension: $9552$
• Sturm bound: $960$

Defining parameters

Level:	\( N \)	\(=\)	\( 912 = 2^{4} \cdot 3 \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 6 \)
Character orbit:	\([\chi]\)	\(=\)	912.cs (of order \(36\) and degree \(12\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 912 \)
Character field:			\(\Q(\zeta_{36})\)
Sturm bound:			\(960\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{6}(912, [\chi])\).

	Total	New	Old
Modular forms	9648	9648	0
Cusp forms	9552	9552	0
Eisenstein series	96	96	0

Trace form

9552 * q - 12 * q^3 - 24 * q^4 - 12 * q^6 - 324 * q^10 - 18 * q^12 - 24 * q^13 - 24 * q^15 - 3684 * q^16 - 24 * q^19 - 1470 * q^21 - 24 * q^22 - 12 * q^24 - 18 * q^27 - 12312 * q^28 + 46572 * q^30 - 72 * q^31 - 24 * q^33 - 24 * q^34 - 12 * q^36 - 24 * q^40 - 137988 * q^42 - 24 * q^43 - 6 * q^45 - 36 * q^46 - 12 * q^48 + 11121408 * q^49 - 12 * q^51 + 27384 * q^52 + 172974 * q^54 - 48 * q^58 + 73110 * q^60 - 24 * q^61 - 201708 * q^63 - 12 * q^64 - 297672 * q^66 - 24 * q^67 - 18 * q^69 + 13500 * q^70 - 614016 * q^72 + 344184 * q^76 - 396 * q^78 - 48 * q^79 - 24 * q^81 - 24 * q^82 - 18 * q^84 + 794376 * q^85 - 36 * q^88 + 213288 * q^90 - 201708 * q^91 - 1470 * q^93 - 2734020 * q^96 - 48 * q^97 + 354282 * q^99

Decomposition of \(S_{6}^{\mathrm{new}}(912, [\chi])\) into newform subspaces

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