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

• Label: 3234.2.j
• Level: $3234$
• Weight: $2$
• Character orbit: 3234.j
• Rep. character: $\chi_{3234}(295,\cdot)$
• Character field: $\Q(\zeta_{5})$
• Dimension: $328$
• Sturm bound: $1344$

Defining parameters

Level:	\( N \)	\(=\)	\( 3234 = 2 \cdot 3 \cdot 7^{2} \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	3234.j (of order \(5\) and degree \(4\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 11 \)
Character field:			\(\Q(\zeta_{5})\)
Sturm bound:			\(1344\)

Dimensions

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

	Total	New	Old
Modular forms	2816	328	2488
Cusp forms	2560	328	2232
Eisenstein series	256	0	256

Trace form

328 * q - 82 * q^4 - 8 * q^5 - 2 * q^6 - 82 * q^9 + 12 * q^10 - 24 * q^11 - 8 * q^13 + 14 * q^15 - 82 * q^16 + 32 * q^17 - 4 * q^19 - 8 * q^20 - 10 * q^22 - 16 * q^23 - 2 * q^24 - 94 * q^25 - 4 * q^26 + 12 * q^29 - 4 * q^30 + 14 * q^31 + 6 * q^33 + 24 * q^34 - 82 * q^36 - 48 * q^37 - 4 * q^38 + 8 * q^39 + 2 * q^40 - 4 * q^41 - 48 * q^43 + 16 * q^44 - 8 * q^45 - 20 * q^46 + 28 * q^47 - 24 * q^50 + 36 * q^51 - 8 * q^52 - 44 * q^53 + 8 * q^54 - 32 * q^55 - 28 * q^57 + 14 * q^58 - 44 * q^59 - 16 * q^60 + 28 * q^61 - 36 * q^62 - 82 * q^64 + 56 * q^65 - 12 * q^66 + 64 * q^67 + 32 * q^68 - 32 * q^69 + 44 * q^71 + 46 * q^73 + 16 * q^74 + 8 * q^75 + 16 * q^76 + 12 * q^79 + 12 * q^80 - 82 * q^81 + 36 * q^82 + 36 * q^83 + 88 * q^85 + 56 * q^86 + 12 * q^87 + 10 * q^88 - 16 * q^89 - 8 * q^90 + 4 * q^92 + 4 * q^93 + 32 * q^94 - 52 * q^95 - 2 * q^96 - 4 * q^97 - 4 * q^99

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

\( S_{2}^{\mathrm{old}}(3234, [\chi]) \simeq \) \(S_{2}^{\mathrm{new}}(22, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(33, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(66, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(77, [\chi])\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(154, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(231, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(462, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(539, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(1078, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(1617, [\chi])\)\(^{\oplus 2}\)