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

• Label: 1305.2.bd
• Level: $1305$
• Weight: $2$
• Character orbit: 1305.bd
• Rep. character: $\chi_{1305}(418,\cdot)$
• Character field: $\Q(\zeta_{12})$
• Dimension: $704$
• Sturm bound: $360$

Defining parameters

Level:	\( N \)	\(=\)	\( 1305 = 3^{2} \cdot 5 \cdot 29 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1305.bd (of order \(12\) and degree \(4\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 1305 \)
Character field:			\(\Q(\zeta_{12})\)
Sturm bound:			\(360\)

Dimensions

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

	Total	New	Old
Modular forms	736	736	0
Cusp forms	704	704	0
Eisenstein series	32	32	0

Trace form

704 * q - 4 * q^2 - 344 * q^4 - 4 * q^7 - 8 * q^9 - 8 * q^11 + 20 * q^14 - 16 * q^15 - 336 * q^16 - 40 * q^17 - 56 * q^18 + 28 * q^20 - 28 * q^21 + 16 * q^22 - 4 * q^23 - 4 * q^25 - 16 * q^26 + 16 * q^28 - 28 * q^30 - 4 * q^31 - 4 * q^32 - 24 * q^33 - 16 * q^34 + 64 * q^36 - 76 * q^38 - 40 * q^39 - 12 * q^40 - 4 * q^42 + 48 * q^44 - 28 * q^45 + 8 * q^46 + 6 * q^50 + 28 * q^52 - 16 * q^53 - 52 * q^55 + 40 * q^56 + 68 * q^57 - 6 * q^58 + 20 * q^60 + 8 * q^61 + 16 * q^62 - 48 * q^63 + 624 * q^64 - 4 * q^65 - 16 * q^66 + 44 * q^68 + 16 * q^70 - 52 * q^72 - 16 * q^73 - 96 * q^75 - 20 * q^76 + 84 * q^77 - 20 * q^78 + 12 * q^79 - 112 * q^80 + 56 * q^81 - 112 * q^82 - 44 * q^83 + 116 * q^84 - 36 * q^85 + 18 * q^87 + 28 * q^88 + 56 * q^89 - 64 * q^90 - 8 * q^92 + 8 * q^93 - 16 * q^95 - 24 * 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.