Space of modular forms of level 2738, weight 2, and Character 2738.l

• Label: 2738.2.l
• Level: $2738$
• Weight: $2$
• Character orbit: 2738.l
• Rep. character: $\chi_{2738}(47,\cdot)$
• Character field: $\Q(\zeta_{111})$
• Dimension: $8568$
• Sturm bound: $703$

Defining parameters

Level:	\( N \)	\(=\)	\( 2738 = 2 \cdot 37^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	2738.l (of order \(111\) and degree \(72\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 1369 \)
Character field:			\(\Q(\zeta_{111})\)
Sturm bound:			\(703\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(2738, [\chi])\).

	Total	New	Old
Modular forms	25416	8568	16848
Cusp forms	25128	8568	16560
Eisenstein series	288	0	288

Trace form

8568 * q + q^2 + 119 * q^4 + 3 * q^5 - 4 * q^7 - 2 * q^8 + 123 * q^9 + 2 * q^10 + 2 * q^13 - 8 * q^14 - 4 * q^15 + 119 * q^16 + 3 * q^17 - 180 * q^18 + 12 * q^19 + 3 * q^20 - 8 * q^21 + 8 * q^22 - 16 * q^23 + 134 * q^25 - 20 * q^26 - 198 * q^27 - 4 * q^28 + 18 * q^29 + 12 * q^30 - 32 * q^31 + q^32 + 4 * q^33 + 361 * q^34 - 16 * q^35 - 246 * q^36 + q^37 - 4 * q^38 - 16 * q^39 - q^40 + 145 * q^41 - 24 * q^42 + 8 * q^43 - 70 * q^45 + 6 * q^46 + 40 * q^47 + 111 * q^49 + 20 * q^50 + 64 * q^51 + 2 * q^52 + 8 * q^53 - 12 * q^54 + 12 * q^55 + 4 * q^56 - 20 * q^57 + 3 * q^58 + 12 * q^59 + 8 * q^60 + 3 * q^61 - 10 * q^62 - 16 * q^63 - 238 * q^64 - 68 * q^65 + 56 * q^66 + 416 * q^67 - 6 * q^68 - 250 * q^69 + 8 * q^70 - 32 * q^71 + 5 * q^72 + 24 * q^73 - 18 * q^74 - 36 * q^75 + 12 * q^76 + 28 * q^77 + 6 * q^78 + 16 * q^79 - 43 * q^80 + 251 * q^81 + 26 * q^82 + 446 * q^83 - 206 * q^84 + 22 * q^85 + 18 * q^86 - 156 * q^87 - 16 * q^88 + 147 * q^89 + 21 * q^90 + 584 * q^91 - 66 * q^92 + 36 * q^93 - 12 * q^94 - 40 * q^95 - 6 * q^97 - 303 * q^98 + 38 * q^99

Decomposition of \(S_{2}^{\mathrm{new}}(2738, [\chi])\) into newform subspaces

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

Decomposition of \(S_{2}^{\mathrm{old}}(2738, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(2738, [\chi]) \simeq \) \(S_{2}^{\mathrm{new}}(1369, [\chi])\)\(^{\oplus 2}\)