Space of modular forms of level 1323, weight 2, and Character 1323.bt

• Label: 1323.2.bt
• Level: $1323$
• Weight: $2$
• Character orbit: 1323.bt
• Rep. character: $\chi_{1323}(62,\cdot)$
• Character field: $\Q(\zeta_{42})$
• Dimension: $648$
• Sturm bound: $336$

Defining parameters

Level:	\( N \)	\(=\)	\( 1323 = 3^{3} \cdot 7^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1323.bt (of order \(42\) and degree \(12\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 441 \)
Character field:			\(\Q(\zeta_{42})\)
Sturm bound:			\(336\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(1323, [\chi])\).

	Total	New	Old
Modular forms	2088	696	1392
Cusp forms	1944	648	1296
Eisenstein series	144	48	96

Trace form

648 * q + 15 * q^2 - 57 * q^4 + 21 * q^5 - 5 * q^7 - 28 * q^10 + 15 * q^11 - 7 * q^13 + 114 * q^14 + 39 * q^16 + 21 * q^20 + 3 * q^22 - 30 * q^23 + 41 * q^25 - 20 * q^28 - 75 * q^29 + 39 * q^32 - 7 * q^34 - 10 * q^37 - 21 * q^38 - 7 * q^40 + 21 * q^41 + 3 * q^43 - 72 * q^46 + 147 * q^47 - 13 * q^49 + 18 * q^50 - 35 * q^52 - 112 * q^55 + 63 * q^56 + 33 * q^58 + 21 * q^59 - 56 * q^61 + 52 * q^64 - 27 * q^65 - 26 * q^67 - 25 * q^70 - 28 * q^73 - 33 * q^74 + 21 * q^76 - 3 * q^77 - 2 * q^79 - 28 * q^82 + 21 * q^83 + 5 * q^85 + 123 * q^86 - 41 * q^88 - 4 * q^91 + 225 * q^92 - 7 * q^94 + 12 * q^95

Decomposition of \(S_{2}^{\mathrm{new}}(1323, [\chi])\) into newform subspaces

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

Decomposition of \(S_{2}^{\mathrm{old}}(1323, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(1323, [\chi]) \simeq \) \(S_{2}^{\mathrm{new}}(441, [\chi])\)\(^{\oplus 2}\)