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

• Label: 1210.2.k
• Level: $1210$
• Weight: $2$
• Character orbit: 1210.k
• Rep. character: $\chi_{1210}(111,\cdot)$
• Character field: $\Q(\zeta_{11})$
• Dimension: $440$
• Sturm bound: $396$

Defining parameters

Level:	\( N \)	\(=\)	\( 1210 = 2 \cdot 5 \cdot 11^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1210.k (of order \(11\) and degree \(10\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 121 \)
Character field:			\(\Q(\zeta_{11})\)
Sturm bound:			\(396\)

Dimensions

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

	Total	New	Old
Modular forms	2020	440	1580
Cusp forms	1940	440	1500
Eisenstein series	80	0	80

Trace form

440 * q + 2 * q^2 + 4 * q^3 - 44 * q^4 + 4 * q^6 + 2 * q^8 + 452 * q^9 + 2 * q^10 + 12 * q^11 - 18 * q^12 - 32 * q^13 - 32 * q^14 - 36 * q^15 - 44 * q^16 + 28 * q^17 + 26 * q^18 + 16 * q^19 + 48 * q^21 + 10 * q^22 + 32 * q^23 + 4 * q^24 - 44 * q^25 + 20 * q^26 + 64 * q^27 + 40 * q^29 + 4 * q^30 - 56 * q^31 + 2 * q^32 + 44 * q^33 + 20 * q^34 + 8 * q^35 - 32 * q^36 + 16 * q^37 + 12 * q^38 + 48 * q^39 - 20 * q^40 + 40 * q^41 + 16 * q^42 + 32 * q^43 + 12 * q^44 + 12 * q^46 + 32 * q^47 + 4 * q^48 - 104 * q^49 + 2 * q^50 + 14 * q^51 + 12 * q^52 - 100 * q^53 + 16 * q^54 + 12 * q^55 + 12 * q^56 + 58 * q^57 - 72 * q^58 + 56 * q^59 + 8 * q^60 + 56 * q^61 + 24 * q^62 + 96 * q^63 - 44 * q^64 + 20 * q^65 + 26 * q^66 - 24 * q^67 + 28 * q^68 + 112 * q^69 + 64 * q^71 + 26 * q^72 - 12 * q^73 + 36 * q^74 + 4 * q^75 - 72 * q^76 - 8 * q^77 + 32 * q^78 - 52 * q^79 + 520 * q^81 - 44 * q^82 + 96 * q^83 + 48 * q^84 - 104 * q^85 + 12 * q^86 + 152 * q^87 - 56 * q^88 + 8 * q^89 - 62 * q^90 - 176 * q^91 - 100 * q^92 - 36 * q^93 - 44 * q^94 + 4 * q^96 - 56 * q^97 - 94 * q^98 + 156 * q^99

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

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