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

• Label: 3234.2.r
• Level: $3234$
• Weight: $2$
• Character orbit: 3234.r
• Rep. character: $\chi_{3234}(463,\cdot)$
• Character field: $\Q(\zeta_{7})$
• Dimension: $576$
• Sturm bound: $1344$

Defining parameters

Level:	\( N \)	\(=\)	\( 3234 = 2 \cdot 3 \cdot 7^{2} \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	3234.r (of order \(7\) and degree \(6\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 49 \)
Character field:			\(\Q(\zeta_{7})\)
Sturm bound:			\(1344\)

Dimensions

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

	Total	New	Old
Modular forms	4080	576	3504
Cusp forms	3984	576	3408
Eisenstein series	96	0	96

Trace form

576 * q - 4 * q^3 - 96 * q^4 - 4 * q^7 - 96 * q^9 - 4 * q^12 - 8 * q^13 - 96 * q^16 - 24 * q^19 - 12 * q^21 - 112 * q^25 - 4 * q^27 - 4 * q^28 - 32 * q^29 - 56 * q^31 - 4 * q^33 - 24 * q^34 - 32 * q^35 - 96 * q^36 + 52 * q^37 - 32 * q^38 + 100 * q^39 + 80 * q^41 + 24 * q^42 - 56 * q^43 + 40 * q^47 + 24 * q^48 - 40 * q^49 - 32 * q^50 + 20 * q^52 + 40 * q^53 - 24 * q^57 + 20 * q^58 + 32 * q^59 + 60 * q^61 + 24 * q^63 - 96 * q^64 - 8 * q^66 - 56 * q^67 - 24 * q^69 - 40 * q^70 - 32 * q^71 - 40 * q^73 - 44 * q^75 - 24 * q^76 - 8 * q^77 + 80 * q^78 - 40 * q^79 - 96 * q^81 - 40 * q^82 + 48 * q^83 - 12 * q^84 - 32 * q^86 - 48 * q^87 - 80 * q^89 + 8 * q^91 - 24 * q^93 - 32 * q^94 - 64 * q^95 + 32 * q^97 - 48 * q^98

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

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