Space of modular forms of level 2704, weight 2, and Character 2704.bh

• Label: 2704.2.bh
• Level: $2704$
• Weight: $2$
• Character orbit: 2704.bh
• Rep. character: $\chi_{2704}(485,\cdot)$
• Character field: $\Q(\zeta_{12})$
• Dimension: $1192$
• Sturm bound: $728$

Defining parameters

Level:	\( N \)	\(=\)	\( 2704 = 2^{4} \cdot 13^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	2704.bh (of order \(12\) and degree \(4\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 208 \)
Character field:			\(\Q(\zeta_{12})\)
Sturm bound:			\(728\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(2704, [\chi])\).

	Total	New	Old
Modular forms	1512	1272	240
Cusp forms	1400	1192	208
Eisenstein series	112	80	32

Trace form

1192 * q + 6 * q^2 + 2 * q^3 + 2 * q^4 + 24 * q^6 + 2 * q^10 + 6 * q^11 - 36 * q^12 - 64 * q^14 + 12 * q^15 + 2 * q^16 + 4 * q^17 + 6 * q^19 + 30 * q^20 - 2 * q^22 - 42 * q^24 - 4 * q^27 + 72 * q^28 + 2 * q^29 - 54 * q^30 - 54 * q^32 + 12 * q^33 + 12 * q^35 + 24 * q^36 + 6 * q^37 - 12 * q^38 + 20 * q^40 - 42 * q^42 - 30 * q^43 + 36 * q^45 + 36 * q^46 + 16 * q^48 - 472 * q^49 + 24 * q^50 - 4 * q^51 - 40 * q^53 + 6 * q^54 + 56 * q^56 + 6 * q^58 - 42 * q^59 + 2 * q^61 + 46 * q^62 + 12 * q^63 + 44 * q^64 - 176 * q^66 + 6 * q^67 + 64 * q^68 + 14 * q^69 - 46 * q^74 + 18 * q^75 + 54 * q^76 - 20 * q^77 + 6 * q^80 + 440 * q^81 - 36 * q^84 - 24 * q^85 - 92 * q^88 + 164 * q^90 - 144 * q^92 - 12 * q^93 - 6 * q^94 - 60 * q^95 + 12 * q^97 - 90 * q^98

Decomposition of \(S_{2}^{\mathrm{new}}(2704, [\chi])\) into newform subspaces

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

Decomposition of \(S_{2}^{\mathrm{old}}(2704, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(2704, [\chi]) \simeq \) \(S_{2}^{\mathrm{new}}(208, [\chi])\)\(^{\oplus 2}\)