Space of modular forms of level 605, weight 6, and Character 605.r

• Label: 605.6.r
• Level: $605$
• Weight: $6$
• Character orbit: 605.r
• Rep. character: $\chi_{605}(32,\cdot)$
• Character field: $\Q(\zeta_{44})$
• Dimension: $6560$
• Sturm bound: $396$

Defining parameters

Level:	\( N \)	\(=\)	\( 605 = 5 \cdot 11^{2} \)
Weight:	\( k \)	\(=\)	\( 6 \)
Character orbit:	\([\chi]\)	\(=\)	605.r (of order \(44\) and degree \(20\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 605 \)
Character field:			\(\Q(\zeta_{44})\)
Sturm bound:			\(396\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{6}(605, [\chi])\).

	Total	New	Old
Modular forms	6640	6640	0
Cusp forms	6560	6560	0
Eisenstein series	80	80	0

Trace form

6560 * q - 22 * q^2 - 40 * q^3 + 26 * q^5 - 44 * q^6 - 22 * q^7 - 22 * q^8 + 5434 * q^10 + 320 * q^11 + 2644 * q^12 - 5786 * q^13 + 774 * q^15 + 164828 * q^16 - 22 * q^17 - 4664 * q^18 - 10934 * q^20 - 44 * q^21 - 23470 * q^22 + 5086 * q^23 + 9530 * q^25 + 3484 * q^26 + 9680 * q^27 - 22 * q^28 - 22 * q^30 - 9716 * q^31 - 22 * q^32 - 33282 * q^33 - 22 * q^35 + 940284 * q^36 - 1888 * q^37 - 184470 * q^38 - 44 * q^41 + 48804 * q^42 - 22 * q^43 + 60104 * q^45 - 44 * q^46 - 26418 * q^47 - 90152 * q^48 - 111012 * q^50 + 15356 * q^51 - 22 * q^52 - 38386 * q^53 + 130900 * q^55 + 393932 * q^56 + 5324 * q^57 + 143594 * q^58 + 119354 * q^60 - 44 * q^61 - 22 * q^62 + 832876 * q^63 - 22 * q^65 - 207044 * q^66 - 14538 * q^67 - 22 * q^68 - 1606 * q^70 - 156676 * q^71 + 726220 * q^72 - 22 * q^73 - 76226 * q^75 - 834284 * q^76 + 341138 * q^77 - 171944 * q^78 + 1645076 * q^80 - 40836000 * q^81 - 179138 * q^82 - 22 * q^83 + 604450 * q^85 - 36116 * q^86 + 5324 * q^87 - 539022 * q^88 + 1299056 * q^90 + 344264 * q^91 + 698262 * q^92 - 201248 * q^93 - 22 * q^95 - 44 * q^96 + 359726 * q^97 - 22 * q^98

Decomposition of \(S_{6}^{\mathrm{new}}(605, [\chi])\) into newform subspaces

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