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

• Label: 2738.2.b
• Level: $2738$
• Weight: $2$
• Character orbit: 2738.b
• Rep. character: $\chi_{2738}(2737,\cdot)$
• Character field: $\Q$
• Dimension: $110$
• Sturm bound: $703$

Defining parameters

Level:	\( N \)	\(=\)	\( 2738 = 2 \cdot 37^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	2738.b (of order \(2\) and degree \(1\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 37 \)
Character field:			\(\Q\)
Sturm bound:			\(703\)

Dimensions

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

	Total	New	Old
Modular forms	390	110	280
Cusp forms	314	110	204
Eisenstein series	76	0	76

Trace form

110 * q + 2 * q^3 - 110 * q^4 + 8 * q^7 + 104 * q^9 + 6 * q^10 - 6 * q^11 - 2 * q^12 + 110 * q^16 - 4 * q^21 - 104 * q^25 + 6 * q^26 + 20 * q^27 - 8 * q^28 - 24 * q^30 + 24 * q^33 - 12 * q^34 - 104 * q^36 + 10 * q^38 - 6 * q^40 - 28 * q^41 + 6 * q^44 + 4 * q^46 + 12 * q^47 + 2 * q^48 + 126 * q^49 - 14 * q^53 - 6 * q^58 + 8 * q^62 + 20 * q^63 - 110 * q^64 - 4 * q^65 + 10 * q^67 - 12 * q^70 - 8 * q^71 - 8 * q^73 - 78 * q^75 + 20 * q^77 + 28 * q^78 + 134 * q^81 - 34 * q^83 + 4 * q^84 + 32 * q^85 + 22 * q^86 + 26 * q^90 + 68 * q^95 - 26 * 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

\( S_{2}^{\mathrm{old}}(2738, [\chi]) \simeq \) \(S_{2}^{\mathrm{new}}(37, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(74, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(1369, [\chi])\)\(^{\oplus 2}\)