Space of modular forms of level 1386, weight 2, and Character 1386.cf

• Label: 1386.2.cf
• Level: $1386$
• Weight: $2$
• Character orbit: 1386.cf
• Rep. character: $\chi_{1386}(29,\cdot)$
• Character field: $\Q(\zeta_{30})$
• Dimension: $576$
• Sturm bound: $576$

Defining parameters

Level:	\( N \)	\(=\)	\( 1386 = 2 \cdot 3^{2} \cdot 7 \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1386.cf (of order \(30\) and degree \(8\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 99 \)
Character field:			\(\Q(\zeta_{30})\)
Sturm bound:			\(576\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(1386, [\chi])\).

	Total	New	Old
Modular forms	2368	576	1792
Cusp forms	2240	576	1664
Eisenstein series	128	0	128

Trace form

576 * q + 8 * q^3 + 72 * q^4 + 12 * q^5 - 10 * q^6 + 16 * q^9 + 18 * q^11 - 24 * q^12 + 72 * q^16 + 20 * q^18 - 60 * q^19 - 12 * q^20 - 6 * q^22 + 10 * q^24 - 60 * q^25 + 32 * q^27 + 180 * q^29 + 60 * q^30 - 12 * q^31 - 4 * q^33 - 12 * q^34 + 22 * q^36 + 24 * q^37 + 120 * q^38 + 100 * q^39 + 48 * q^45 - 12 * q^47 - 4 * q^48 - 72 * q^49 - 10 * q^51 + 20 * q^57 + 114 * q^59 + 8 * q^60 - 144 * q^64 - 32 * q^66 + 60 * q^67 + 40 * q^69 + 50 * q^75 + 128 * q^78 - 104 * q^81 + 36 * q^82 - 180 * q^83 - 40 * q^84 - 102 * q^86 - 6 * q^88 - 200 * q^90 + 72 * q^91 - 176 * q^93 - 240 * q^95 + 30 * q^97 + 220 * q^99

Decomposition of \(S_{2}^{\mathrm{new}}(1386, [\chi])\) into newform subspaces

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

Decomposition of \(S_{2}^{\mathrm{old}}(1386, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(1386, [\chi]) \simeq \) \(S_{2}^{\mathrm{new}}(99, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(198, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(693, [\chi])\)\(^{\oplus 2}\)