Space of modular forms of level 1125, weight 2, and Character 1125.v

• Label: 1125.2.v
• Level: $1125$
• Weight: $2$
• Character orbit: 1125.v
• Rep. character: $\chi_{1125}(49,\cdot)$
• Character field: $\Q(\zeta_{30})$
• Dimension: $672$
• Sturm bound: $300$

Defining parameters

Level:	\( N \)	\(=\)	\( 1125 = 3^{2} \cdot 5^{3} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1125.v (of order \(30\) and degree \(8\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 225 \)
Character field:			\(\Q(\zeta_{30})\)
Sturm bound:			\(300\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(1125, [\chi])\).

	Total	New	Old
Modular forms	1280	768	512
Cusp forms	1120	672	448
Eisenstein series	160	96	64

Trace form

672 * q + 5 * q^2 + 10 * q^3 - 75 * q^4 - 22 * q^6 + 20 * q^8 + 8 * q^9 - 17 * q^11 + 30 * q^12 + 5 * q^13 - 25 * q^14 + 61 * q^16 + 20 * q^17 + 12 * q^19 + 3 * q^21 + 5 * q^22 + 5 * q^23 + 14 * q^24 - 200 * q^26 + 25 * q^27 + 60 * q^28 + 15 * q^29 - 3 * q^31 + 35 * q^33 - 9 * q^34 + 10 * q^36 + 20 * q^37 + 75 * q^38 - 8 * q^39 - 25 * q^41 + 140 * q^42 + 12 * q^44 - 44 * q^46 - 20 * q^47 - 165 * q^48 + 200 * q^49 - 58 * q^51 + 15 * q^52 + 20 * q^53 - 45 * q^54 - 98 * q^56 + 5 * q^58 + 30 * q^59 - 9 * q^61 - 40 * q^62 + 76 * q^64 - 170 * q^66 - 10 * q^67 - 22 * q^69 - 22 * q^71 - 40 * q^72 + 20 * q^73 - 98 * q^74 - 8 * q^76 + 115 * q^77 - 110 * q^78 + 15 * q^79 - 136 * q^81 - 65 * q^83 - 173 * q^84 + 3 * q^86 - 115 * q^87 + 5 * q^88 - 186 * q^89 + 6 * q^91 - 95 * q^92 - 9 * q^94 + 23 * q^96 + 5 * q^97 + 70 * q^98 + 40 * q^99

Decomposition of \(S_{2}^{\mathrm{new}}(1125, [\chi])\) into newform subspaces

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

Decomposition of \(S_{2}^{\mathrm{old}}(1125, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(1125, [\chi]) \simeq \) \(S_{2}^{\mathrm{new}}(225, [\chi])\)\(^{\oplus 2}\)