Space of modular forms of level 1197, weight 2, and Character 1197.dp

• Label: 1197.2.dp
• Level: $1197$
• Weight: $2$
• Character orbit: 1197.dp
• Rep. character: $\chi_{1197}(787,\cdot)$
• Character field: $\Q(\zeta_{6})$
• Dimension: $312$
• Sturm bound: $320$

Defining parameters

Level:	\( N \)	\(=\)	\( 1197 = 3^{2} \cdot 7 \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1197.dp (of order \(6\) and degree \(2\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 1197 \)
Character field:			\(\Q(\zeta_{6})\)
Sturm bound:			\(320\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(1197, [\chi])\).

	Total	New	Old
Modular forms	328	328	0
Cusp forms	312	312	0
Eisenstein series	16	16	0

Trace form

312 * q + 3 * q^2 - 3 * q^3 + 151 * q^4 + 3 * q^5 - 3 * q^7 + q^9 - 12 * q^10 - 4 * q^11 - 12 * q^12 - 6 * q^13 - 3 * q^14 - 9 * q^15 - 143 * q^16 + 3 * q^17 - 12 * q^18 - 6 * q^19 - 18 * q^20 + 6 * q^21 - 18 * q^22 + 3 * q^23 + 30 * q^24 + 139 * q^25 - 18 * q^26 - 14 * q^28 - 6 * q^29 - 17 * q^30 + 12 * q^31 - 9 * q^32 - 6 * q^33 - 13 * q^35 + 22 * q^36 - 3 * q^37 - 30 * q^38 - 24 * q^39 - 68 * q^42 + 4 * q^43 + 17 * q^44 - 24 * q^45 - 12 * q^46 - 45 * q^48 - 3 * q^49 - 9 * q^50 - 3 * q^51 - 9 * q^52 - 6 * q^54 - 15 * q^55 + 24 * q^56 - 23 * q^57 + 4 * q^58 + 24 * q^59 + 3 * q^60 + 126 * q^62 - 28 * q^63 - 268 * q^64 + 6 * q^65 - 90 * q^66 - 18 * q^67 - 9 * q^69 - 3 * q^70 - 27 * q^71 + 63 * q^72 - 6 * q^73 + 15 * q^74 + 135 * q^75 - 12 * q^76 - 44 * q^77 + 21 * q^78 + 6 * q^79 - 23 * q^81 - 18 * q^82 + 87 * q^84 + 16 * q^85 - 57 * q^86 + 18 * q^87 - 6 * q^89 + 84 * q^90 - 27 * q^91 + 144 * q^92 + 40 * q^93 - 49 * q^95 + 144 * q^96 - 9 * q^98 - 79 * q^99

Decomposition of \(S_{2}^{\mathrm{new}}(1197, [\chi])\) into newform subspaces

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