Space of modular forms of level 1225, weight 2, and Character 1225.bu

• Label: 1225.2.bu
• Level: $1225$
• Weight: $2$
• Character orbit: 1225.bu
• Rep. character: $\chi_{1225}(3,\cdot)$
• Character field: $\Q(\zeta_{420})$
• Dimension: $13248$
• Sturm bound: $280$

Defining parameters

Level:	\( N \)	\(=\)	\( 1225 = 5^{2} \cdot 7^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1225.bu (of order \(420\) and degree \(96\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 1225 \)
Character field:			\(\Q(\zeta_{420})\)
Sturm bound:			\(280\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(1225, [\chi])\).

	Total	New	Old
Modular forms	13632	13632	0
Cusp forms	13248	13248	0
Eisenstein series	384	384	0

Trace form

13248 * q - 104 * q^2 - 88 * q^3 - 130 * q^4 - 82 * q^5 - 84 * q^6 - 102 * q^7 - 76 * q^8 - 130 * q^9 - 76 * q^10 - 78 * q^11 - 76 * q^12 - 112 * q^13 - 120 * q^14 - 112 * q^15 + 186 * q^16 - 14 * q^17 - 50 * q^18 - 180 * q^19 - 112 * q^20 - 72 * q^21 - 52 * q^22 - 96 * q^23 - 106 * q^25 - 176 * q^26 - 112 * q^27 - 134 * q^28 - 100 * q^29 - 50 * q^30 - 108 * q^31 - 184 * q^32 - 82 * q^33 - 140 * q^34 - 110 * q^35 - 604 * q^36 - 110 * q^37 - 212 * q^38 - 130 * q^39 - 64 * q^40 - 84 * q^41 - 6 * q^42 + 4 * q^43 - 130 * q^44 + 150 * q^45 - 78 * q^46 - 16 * q^47 - 1024 * q^50 - 208 * q^51 - 328 * q^52 - 24 * q^53 - 110 * q^54 - 154 * q^55 - 88 * q^56 - 12 * q^57 + 12 * q^58 - 230 * q^59 - 104 * q^60 - 66 * q^61 - 84 * q^62 - 46 * q^63 - 40 * q^64 - 110 * q^65 + 6 * q^66 - 52 * q^67 - 510 * q^68 - 140 * q^69 - 220 * q^70 - 60 * q^71 - 328 * q^72 - 106 * q^73 - 244 * q^75 - 336 * q^76 - 32 * q^77 + 164 * q^78 - 60 * q^79 - 162 * q^80 + 166 * q^81 - 188 * q^82 + 168 * q^83 - 1000 * q^84 - 64 * q^85 - 78 * q^86 - 36 * q^87 - 418 * q^88 + 90 * q^89 - 448 * q^90 - 72 * q^91 - 92 * q^92 - 498 * q^93 - 110 * q^94 - 156 * q^95 + 6 * q^96 + 1276 * q^98

Decomposition of \(S_{2}^{\mathrm{new}}(1225, [\chi])\) into newform subspaces

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