Space of modular forms of level 1305, weight 2, and Character 1305.db

• Label: 1305.2.db
• Level: $1305$
• Weight: $2$
• Character orbit: 1305.db
• Rep. character: $\chi_{1305}(292,\cdot)$
• Character field: $\Q(\zeta_{84})$
• Dimension: $4224$
• Sturm bound: $360$

Defining parameters

Level:	\( N \)	\(=\)	\( 1305 = 3^{2} \cdot 5 \cdot 29 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1305.db (of order \(84\) and degree \(24\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 1305 \)
Character field:			\(\Q(\zeta_{84})\)
Sturm bound:			\(360\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(1305, [\chi])\).

	Total	New	Old
Modular forms	4416	4416	0
Cusp forms	4224	4224	0
Eisenstein series	192	192	0

Trace form

4224 * q - 10 * q^2 - 28 * q^3 + 344 * q^4 - 14 * q^5 - 56 * q^6 - 10 * q^7 - 56 * q^8 + 8 * q^9 - 56 * q^10 - 20 * q^11 - 14 * q^13 - 20 * q^14 - 12 * q^15 + 308 * q^16 - 72 * q^17 - 168 * q^18 - 42 * q^20 - 56 * q^21 - 30 * q^22 - 10 * q^23 - 56 * q^24 - 10 * q^25 - 96 * q^26 + 14 * q^27 - 16 * q^28 - 28 * q^30 - 24 * q^31 - 10 * q^32 - 4 * q^33 - 40 * q^34 - 56 * q^35 + 48 * q^36 - 56 * q^37 - 134 * q^38 + 40 * q^39 - 2 * q^40 - 28 * q^41 - 24 * q^42 - 14 * q^43 + 176 * q^44 - 120 * q^46 - 14 * q^47 - 84 * q^48 + 84 * q^49 - 20 * q^50 - 56 * q^51 - 42 * q^52 - 40 * q^53 - 4 * q^55 - 68 * q^56 - 68 * q^57 - 8 * q^58 - 118 * q^60 - 36 * q^61 - 72 * q^62 + 20 * q^63 - 624 * q^64 - 10 * q^65 - 40 * q^66 - 14 * q^67 - 114 * q^68 + 112 * q^69 - 30 * q^70 - 112 * q^71 + 24 * q^72 - 40 * q^73 + 112 * q^74 - 2 * q^75 - 8 * q^76 - 98 * q^77 + 132 * q^78 - 12 * q^79 - 336 * q^80 - 112 * q^81 + 30 * q^83 - 312 * q^84 - 48 * q^85 - 88 * q^87 - 56 * q^88 - 56 * q^89 - 104 * q^90 - 112 * q^91 - 34 * q^92 - 36 * q^93 - 84 * q^94 - 334 * q^95 - 56 * q^96 - 182 * q^97 - 56 * q^98 - 88 * q^99

Decomposition of \(S_{2}^{\mathrm{new}}(1305, [\chi])\) into newform subspaces

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