Space of modular forms of level 325, weight 4, and Character 325.z

• Label: 325.4.z
• Level: $325$
• Weight: $4$
• Character orbit: 325.z
• Rep. character: $\chi_{325}(8,\cdot)$
• Character field: $\Q(\zeta_{20})$
• Dimension: $824$
• Sturm bound: $140$

Defining parameters

Level:	\( N \)	\(=\)	\( 325 = 5^{2} \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	325.z (of order \(20\) and degree \(8\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 325 \)
Character field:			\(\Q(\zeta_{20})\)
Sturm bound:			\(140\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{4}(325, [\chi])\).

	Total	New	Old
Modular forms	856	856	0
Cusp forms	824	824	0
Eisenstein series	32	32	0

Trace form

824 * q - 10 * q^2 - 16 * q^3 - 808 * q^4 + 6 * q^5 - 6 * q^6 - 22 * q^8 - 20 * q^9 + 32 * q^10 - 6 * q^11 + 56 * q^12 + 94 * q^13 - 20 * q^14 + 314 * q^15 - 3116 * q^16 - 182 * q^17 + 110 * q^19 - 694 * q^20 + 264 * q^21 + 460 * q^22 - 120 * q^23 + 140 * q^24 - 454 * q^25 - 16 * q^26 + 152 * q^27 + 630 * q^28 + 60 * q^29 + 656 * q^30 - 6 * q^31 + 1724 * q^32 - 690 * q^33 - 1598 * q^34 - 4 * q^35 + 160 * q^36 - 1950 * q^37 + 32 * q^38 - 2450 * q^39 + 1152 * q^40 + 244 * q^41 - 388 * q^42 + 1208 * q^43 + 22 * q^44 - 1984 * q^45 - 6 * q^46 + 1890 * q^47 + 540 * q^48 - 35672 * q^49 - 4896 * q^50 + 4704 * q^52 - 1226 * q^53 - 3586 * q^54 + 1544 * q^55 + 6860 * q^56 - 2828 * q^57 + 6830 * q^58 - 10 * q^59 + 426 * q^60 - 12 * q^61 - 484 * q^62 + 5356 * q^63 - 11488 * q^64 + 1348 * q^65 - 12 * q^66 + 986 * q^67 - 1996 * q^68 + 7932 * q^70 - 6 * q^71 + 900 * q^72 - 1926 * q^73 + 4016 * q^75 + 240 * q^76 + 6264 * q^77 + 1190 * q^78 - 20 * q^79 - 10168 * q^80 + 14082 * q^81 + 4004 * q^82 + 130 * q^83 + 1972 * q^84 + 3042 * q^85 + 74 * q^86 + 1140 * q^87 + 8672 * q^88 + 3460 * q^89 + 2820 * q^90 - 536 * q^91 - 848 * q^92 - 11060 * q^94 - 192 * q^95 - 12696 * q^96 + 6574 * q^97 + 848 * q^98 + 108 * q^99

Decomposition of \(S_{4}^{\mathrm{new}}(325, [\chi])\) into newform subspaces

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