Space of modular forms of level 1210, weight 2, and Character 1210.g

• Label: 1210.2.g
• Level: $1210$
• Weight: $2$
• Character orbit: 1210.g
• Rep. character: $\chi_{1210}(81,\cdot)$
• Character field: $\Q(\zeta_{5})$
• Dimension: $144$
• Sturm bound: $396$

Defining parameters

Level:	\( N \)	\(=\)	\( 1210 = 2 \cdot 5 \cdot 11^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1210.g (of order \(5\) and degree \(4\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 11 \)
Character field:			\(\Q(\zeta_{5})\)
Sturm bound:			\(396\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(1210, [\chi])\).

	Total	New	Old
Modular forms	888	144	744
Cusp forms	696	144	552
Eisenstein series	192	0	192

Trace form

144 * q - 2 * q^2 - 4 * q^3 - 36 * q^4 + 6 * q^6 - 2 * q^8 - 28 * q^9 + 8 * q^10 - 4 * q^12 + 8 * q^13 - 2 * q^14 + 12 * q^15 - 36 * q^16 - 8 * q^17 - 16 * q^18 + 14 * q^19 - 48 * q^21 + 6 * q^24 - 36 * q^25 + 12 * q^26 + 26 * q^27 + 40 * q^29 - 4 * q^30 + 8 * q^32 + 44 * q^34 - 8 * q^35 - 38 * q^36 + 8 * q^37 - 20 * q^38 + 32 * q^39 - 2 * q^40 + 30 * q^41 + 8 * q^42 - 12 * q^43 + 8 * q^46 - 36 * q^47 - 4 * q^48 - 86 * q^49 - 2 * q^50 - 10 * q^51 - 12 * q^52 - 8 * q^53 - 16 * q^54 - 12 * q^56 - 70 * q^57 - 40 * q^58 - 62 * q^59 - 8 * q^60 + 24 * q^61 - 4 * q^62 + 44 * q^63 - 36 * q^64 + 20 * q^65 + 44 * q^67 - 8 * q^68 + 12 * q^69 + 8 * q^71 + 14 * q^72 + 24 * q^73 + 4 * q^74 + 6 * q^75 - 16 * q^76 + 96 * q^78 - 58 * q^81 + 10 * q^82 + 34 * q^83 + 12 * q^84 - 28 * q^85 - 42 * q^86 + 48 * q^87 - 26 * q^90 + 94 * q^91 + 20 * q^92 + 144 * q^93 + 26 * q^94 - 4 * q^96 + 142 * q^97 + 8 * q^98

Decomposition of \(S_{2}^{\mathrm{new}}(1210, [\chi])\) into newform subspaces

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

Decomposition of \(S_{2}^{\mathrm{old}}(1210, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(1210, [\chi]) \simeq \) \(S_{2}^{\mathrm{new}}(22, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(55, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(110, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(121, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(242, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(605, [\chi])\)\(^{\oplus 2}\)