Space of modular forms of level 3234, weight 2, and Character 3234.i

• Label: 3234.2.i
• Level: $3234$
• Weight: $2$
• Character orbit: 3234.i
• Rep. character: $\chi_{3234}(67,\cdot)$
• Character field: $\Q(\zeta_{3})$
• Dimension: $136$
• Sturm bound: $1344$

Defining parameters

Level:	\( N \)	\(=\)	\( 3234 = 2 \cdot 3 \cdot 7^{2} \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	3234.i (of order \(3\) and degree \(2\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 7 \)
Character field:			\(\Q(\zeta_{3})\)
Sturm bound:			\(1344\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(3234, [\chi])\).

	Total	New	Old
Modular forms	1408	136	1272
Cusp forms	1280	136	1144
Eisenstein series	128	0	128

Trace form

136 * q - 68 * q^4 - 68 * q^9 - 68 * q^16 - 8 * q^19 + 32 * q^23 - 44 * q^25 - 32 * q^29 + 4 * q^33 - 24 * q^34 + 136 * q^36 - 44 * q^37 - 16 * q^38 - 48 * q^39 - 64 * q^41 + 16 * q^43 + 16 * q^46 - 8 * q^47 + 128 * q^50 + 16 * q^51 - 24 * q^53 + 80 * q^57 - 36 * q^58 - 16 * q^59 - 8 * q^61 + 136 * q^64 - 16 * q^65 + 8 * q^66 - 40 * q^67 - 24 * q^69 - 32 * q^71 - 16 * q^73 - 16 * q^74 - 8 * q^75 + 16 * q^76 + 16 * q^79 - 68 * q^81 + 16 * q^82 - 32 * q^83 + 208 * q^85 + 16 * q^86 - 24 * q^87 - 40 * q^89 - 64 * q^92 - 40 * q^93 - 16 * q^94 + 64 * q^95 - 120 * q^97

Decomposition of \(S_{2}^{\mathrm{new}}(3234, [\chi])\) into newform subspaces

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

Decomposition of \(S_{2}^{\mathrm{old}}(3234, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(3234, [\chi]) \simeq \) \(S_{2}^{\mathrm{new}}(21, [\chi])\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(42, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(49, [\chi])\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(77, [\chi])\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(98, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(147, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(154, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(231, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(294, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(462, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(539, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(1078, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(1617, [\chi])\)\(^{\oplus 2}\)