Space of modular forms of level 164, weight 5, and Character 164.j

• Label: 164.5.j
• Level: $164$
• Weight: $5$
• Character orbit: 164.j
• Rep. character: $\chi_{164}(51,\cdot)$
• Character field: $\Q(\zeta_{10})$
• Dimension: $328$
• Sturm bound: $105$

Defining parameters

Level:	\( N \)	\(=\)	\( 164 = 2^{2} \cdot 41 \)
Weight:	\( k \)	\(=\)	\( 5 \)
Character orbit:	\([\chi]\)	\(=\)	164.j (of order \(10\) and degree \(4\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 164 \)
Character field:			\(\Q(\zeta_{10})\)
Sturm bound:			\(105\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{5}(164, [\chi])\).

	Total	New	Old
Modular forms	344	344	0
Cusp forms	328	328	0
Eisenstein series	16	16	0

Trace form

328 * q - 3 * q^2 - 3 * q^4 + 18 * q^5 + 111 * q^6 - 282 * q^8 - 8552 * q^9 + 98 * q^10 + 630 * q^12 + 114 * q^13 + 50 * q^14 - 283 * q^16 - 654 * q^17 + 738 * q^18 + 1076 * q^20 + 1088 * q^21 + 761 * q^22 + 1644 * q^24 - 8416 * q^25 - 1027 * q^26 - 3140 * q^28 + 738 * q^29 + 1126 * q^30 + 712 * q^32 - 4040 * q^33 + 653 * q^34 - 6332 * q^36 - 2106 * q^37 - 13180 * q^38 + 14094 * q^40 + 3028 * q^41 - 5096 * q^42 + 2210 * q^44 - 7310 * q^45 - 11570 * q^46 - 1721 * q^48 + 26980 * q^49 - 688 * q^50 - 10449 * q^52 + 2514 * q^53 - 5950 * q^54 - 25907 * q^56 - 6912 * q^57 - 16750 * q^58 - 19012 * q^60 + 2194 * q^61 - 194 * q^62 - 19122 * q^64 + 682 * q^65 + 116 * q^66 - 17760 * q^68 + 6976 * q^69 - 1543 * q^70 + 19909 * q^72 + 13736 * q^73 + 30821 * q^74 + 47812 * q^76 - 9610 * q^77 + 20674 * q^78 + 25469 * q^80 + 180648 * q^81 - 21097 * q^82 + 33104 * q^84 + 33612 * q^85 - 67565 * q^86 + 7580 * q^88 - 62910 * q^89 - 29422 * q^90 - 44351 * q^92 + 39552 * q^93 + 34844 * q^94 - 39108 * q^96 - 46386 * q^97 + 4886 * q^98

Decomposition of \(S_{5}^{\mathrm{new}}(164, [\chi])\) into newform subspaces

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