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

• Label: 1225.2.bi
• Level: $1225$
• Weight: $2$
• Character orbit: 1225.bi
• Rep. character: $\chi_{1225}(117,\cdot)$
• Character field: $\Q(\zeta_{60})$
• Dimension: $1536$
• Sturm bound: $280$

Defining parameters

Level:	\( N \)	\(=\)	\( 1225 = 5^{2} \cdot 7^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1225.bi (of order \(60\) and degree \(16\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 175 \)
Character field:			\(\Q(\zeta_{60})\)
Sturm bound:			\(280\)

Dimensions

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

	Total	New	Old
Modular forms	2368	1664	704
Cusp forms	2112	1536	576
Eisenstein series	256	128	128

Trace form

1536 * q + 8 * q^2 + 24 * q^3 + 10 * q^4 + 30 * q^5 - 60 * q^8 + 10 * q^9 + 36 * q^10 + 6 * q^11 + 36 * q^12 - 68 * q^15 - 162 * q^16 + 42 * q^17 + 46 * q^18 + 30 * q^19 - 192 * q^22 + 64 * q^23 - 10 * q^25 + 48 * q^26 - 160 * q^29 + 110 * q^30 + 18 * q^31 - 52 * q^32 + 30 * q^33 + 224 * q^36 + 18 * q^37 - 72 * q^38 - 70 * q^39 + 48 * q^40 + 4 * q^43 + 10 * q^44 - 186 * q^45 + 6 * q^46 + 54 * q^47 + 192 * q^50 + 16 * q^51 - 216 * q^52 + 106 * q^53 + 30 * q^54 + 152 * q^57 - 60 * q^58 - 90 * q^59 - 200 * q^60 + 18 * q^61 - 20 * q^64 - 30 * q^65 + 90 * q^66 - 12 * q^67 - 342 * q^68 - 48 * q^71 + 138 * q^72 + 6 * q^73 - 216 * q^75 - 140 * q^78 + 10 * q^79 + 6 * q^80 - 122 * q^81 - 216 * q^82 - 48 * q^85 + 6 * q^86 + 48 * q^87 + 266 * q^88 - 120 * q^89 - 108 * q^92 - 182 * q^93 + 30 * q^94 + 110 * q^95 + 90 * q^96

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

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

Decomposition of \(S_{2}^{\mathrm{old}}(1225, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(1225, [\chi]) \simeq \) \(S_{2}^{\mathrm{new}}(175, [\chi])\)\(^{\oplus 2}\)