Space of modular forms of level 425, weight 4, and Character 425.k

• Label: 425.4.k
• Level: $425$
• Weight: $4$
• Character orbit: 425.k
• Rep. character: $\chi_{425}(86,\cdot)$
• Character field: $\Q(\zeta_{5})$
• Dimension: $480$
• Sturm bound: $180$

Defining parameters

Level:	\( N \)	\(=\)	\( 425 = 5^{2} \cdot 17 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	425.k (of order \(5\) and degree \(4\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 25 \)
Character field:			\(\Q(\zeta_{5})\)
Sturm bound:			\(180\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{4}(425, [\chi])\).

	Total	New	Old
Modular forms	552	480	72
Cusp forms	536	480	56
Eisenstein series	16	0	16

Trace form

480 * q + 8 * q^3 - 480 * q^4 + 32 * q^5 + 24 * q^6 + 24 * q^7 - 126 * q^8 - 1144 * q^9 + 54 * q^10 + 88 * q^11 - 144 * q^12 + 48 * q^13 - 20 * q^14 - 500 * q^15 - 1704 * q^16 + 508 * q^18 + 36 * q^19 + 42 * q^20 - 1158 * q^22 - 704 * q^23 - 1180 * q^24 - 68 * q^25 + 20 * q^26 - 916 * q^27 - 1068 * q^28 + 300 * q^29 - 344 * q^30 + 1272 * q^31 + 792 * q^32 - 688 * q^33 + 136 * q^34 + 760 * q^35 - 5674 * q^36 + 192 * q^37 + 3524 * q^38 + 2368 * q^39 - 772 * q^40 + 368 * q^41 + 3970 * q^42 + 24 * q^43 + 880 * q^44 - 628 * q^45 + 1208 * q^46 - 3016 * q^47 - 3580 * q^48 + 22296 * q^49 - 5574 * q^50 - 1632 * q^51 - 3606 * q^52 + 1560 * q^53 - 240 * q^54 - 2072 * q^55 + 4044 * q^56 + 3440 * q^57 - 2760 * q^58 + 1896 * q^59 + 18900 * q^60 + 732 * q^61 + 1558 * q^62 + 5796 * q^63 - 1182 * q^64 - 320 * q^65 - 3632 * q^66 + 4656 * q^67 - 3904 * q^69 + 340 * q^70 + 3924 * q^71 - 12938 * q^72 - 3048 * q^73 - 10148 * q^74 - 5584 * q^75 - 304 * q^76 - 6200 * q^77 + 3388 * q^78 - 260 * q^79 - 18864 * q^80 - 3328 * q^81 + 10756 * q^82 + 3200 * q^83 + 4484 * q^84 - 408 * q^85 - 3116 * q^86 + 1976 * q^87 + 21256 * q^88 + 4240 * q^89 - 1756 * q^90 - 152 * q^91 + 12346 * q^92 - 800 * q^93 - 6624 * q^94 - 7284 * q^95 + 10764 * q^96 - 12828 * q^97 - 7202 * q^98 - 7616 * q^99

Decomposition of \(S_{4}^{\mathrm{new}}(425, [\chi])\) into newform subspaces

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

Decomposition of \(S_{4}^{\mathrm{old}}(425, [\chi])\) into lower level spaces

\( S_{4}^{\mathrm{old}}(425, [\chi]) \simeq \) \(S_{4}^{\mathrm{new}}(25, [\chi])\)\(^{\oplus 2}\)