Space of modular forms of level 608, weight 3, and Character 608.bk

• Label: 608.3.bk
• Level: $608$
• Weight: $3$
• Character orbit: 608.bk
• Rep. character: $\chi_{608}(11,\cdot)$
• Character field: $\Q(\zeta_{24})$
• Dimension: $1264$
• Sturm bound: $240$

Defining parameters

Level:	\( N \)	\(=\)	\( 608 = 2^{5} \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	608.bk (of order \(24\) and degree \(8\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 608 \)
Character field:			\(\Q(\zeta_{24})\)
Sturm bound:			\(240\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{3}(608, [\chi])\).

	Total	New	Old
Modular forms	1296	1296	0
Cusp forms	1264	1264	0
Eisenstein series	32	32	0

Trace form

1264 * q - 4 * q^2 - 4 * q^3 - 4 * q^4 - 4 * q^5 - 4 * q^6 - 16 * q^7 - 16 * q^8 - 4 * q^9 - 44 * q^10 - 16 * q^11 - 16 * q^12 - 4 * q^13 - 4 * q^14 - 8 * q^15 - 4 * q^16 - 16 * q^18 - 8 * q^19 - 16 * q^20 - 4 * q^21 - 4 * q^22 - 4 * q^23 - 148 * q^24 - 4 * q^25 - 216 * q^26 - 16 * q^27 - 124 * q^28 - 4 * q^29 + 16 * q^30 + 36 * q^32 - 8 * q^33 - 96 * q^34 - 196 * q^35 - 4 * q^36 - 16 * q^37 - 36 * q^38 - 16 * q^39 - 184 * q^40 - 4 * q^41 - 204 * q^42 - 4 * q^43 - 136 * q^44 + 56 * q^45 + 48 * q^46 - 8 * q^47 - 4 * q^48 + 608 * q^50 + 116 * q^51 + 156 * q^52 - 4 * q^53 + 592 * q^54 - 4 * q^55 - 736 * q^56 - 8 * q^57 - 16 * q^58 - 4 * q^59 + 200 * q^60 + 124 * q^61 - 12 * q^62 + 440 * q^64 - 32 * q^65 + 732 * q^66 - 4 * q^67 + 232 * q^68 + 752 * q^69 - 340 * q^70 - 4 * q^71 - 4 * q^72 - 4 * q^73 - 4 * q^74 + 184 * q^75 + 504 * q^76 - 16 * q^77 - 4 * q^78 + 1016 * q^79 - 36 * q^80 + 116 * q^82 - 16 * q^83 - 16 * q^84 - 204 * q^85 - 452 * q^86 + 880 * q^87 - 576 * q^88 - 4 * q^89 + 644 * q^90 - 4 * q^91 - 4 * q^92 + 32 * q^93 + 1600 * q^94 + 800 * q^96 - 8 * q^97 - 400 * q^98 - 188 * q^99

Decomposition of \(S_{3}^{\mathrm{new}}(608, [\chi])\) into newform subspaces

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