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

• Label: 1210.2.j
• Level: $1210$
• Weight: $2$
• Character orbit: 1210.j
• Rep. character: $\chi_{1210}(9,\cdot)$
• Character field: $\Q(\zeta_{10})$
• Dimension: $216$
• Sturm bound: $396$

Defining parameters

Level:	\( N \)	\(=\)	\( 1210 = 2 \cdot 5 \cdot 11^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1210.j (of order \(10\) and degree \(4\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 55 \)
Character field:			\(\Q(\zeta_{10})\)
Sturm bound:			\(396\)

Dimensions

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

	Total	New	Old
Modular forms	888	216	672
Cusp forms	696	216	480
Eisenstein series	192	0	192

Trace form

216 * q + 54 * q^4 - 4 * q^6 + 74 * q^9 + 4 * q^10 + 6 * q^14 - 14 * q^15 - 54 * q^16 + 16 * q^19 + 40 * q^21 + 4 * q^24 + 12 * q^25 + 4 * q^26 + 4 * q^29 + 26 * q^30 - 4 * q^31 - 8 * q^34 + 52 * q^35 - 54 * q^36 + 36 * q^39 + 6 * q^40 - 46 * q^41 - 52 * q^45 - 32 * q^46 - 8 * q^49 + 4 * q^50 - 12 * q^51 - 64 * q^54 + 4 * q^56 + 4 * q^59 - 16 * q^60 - 56 * q^61 + 54 * q^64 - 44 * q^65 - 48 * q^69 - 16 * q^70 + 80 * q^71 - 56 * q^75 + 4 * q^76 + 4 * q^79 - 10 * q^80 + 86 * q^81 + 20 * q^84 + 38 * q^85 + 8 * q^86 + 188 * q^89 - 10 * q^90 - 2 * q^91 + 30 * q^94 + 50 * q^95 - 4 * q^96

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

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