Space of modular forms of level 1776, weight 2, and Character 1776.ba

• Label: 1776.2.ba
• Level: $1776$
• Weight: $2$
• Character orbit: 1776.ba
• Rep. character: $\chi_{1776}(445,\cdot)$
• Character field: $\Q(\zeta_{4})$
• Dimension: $288$
• Sturm bound: $608$

Defining parameters

Level:	\( N \)	\(=\)	\( 1776 = 2^{4} \cdot 3 \cdot 37 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1776.ba (of order \(4\) and degree \(2\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 16 \)
Character field:			\(\Q(i)\)
Sturm bound:			\(608\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(1776, [\chi])\).

	Total	New	Old
Modular forms	616	288	328
Cusp forms	600	288	312
Eisenstein series	16	0	16

Trace form

288 * q + 24 * q^8 + 16 * q^10 - 16 * q^12 - 32 * q^14 + 16 * q^15 + 8 * q^16 + 16 * q^19 - 32 * q^20 + 8 * q^22 - 8 * q^24 - 40 * q^26 - 16 * q^28 + 16 * q^30 - 48 * q^31 + 40 * q^32 + 24 * q^34 - 48 * q^35 + 8 * q^36 - 40 * q^38 - 56 * q^40 + 32 * q^43 + 32 * q^44 + 16 * q^46 + 16 * q^48 - 288 * q^49 + 16 * q^50 - 16 * q^51 + 32 * q^52 - 8 * q^54 - 16 * q^58 - 64 * q^59 - 32 * q^61 + 72 * q^62 - 24 * q^64 + 48 * q^67 + 40 * q^68 - 32 * q^69 - 16 * q^70 - 32 * q^75 + 48 * q^76 - 24 * q^78 + 48 * q^79 - 104 * q^80 - 288 * q^81 - 80 * q^82 + 80 * q^83 + 48 * q^84 + 32 * q^85 + 32 * q^86 + 16 * q^88 + 16 * q^90 + 16 * q^91 - 72 * q^92 - 24 * q^94 + 96 * q^95 - 24 * q^98

Decomposition of \(S_{2}^{\mathrm{new}}(1776, [\chi])\) into newform subspaces

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

Decomposition of \(S_{2}^{\mathrm{old}}(1776, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(1776, [\chi]) \simeq \) \(S_{2}^{\mathrm{new}}(16, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(48, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(592, [\chi])\)\(^{\oplus 2}\)