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

• Label: 3234.2.by
• Level: $3234$
• Weight: $2$
• Character orbit: 3234.by
• Rep. character: $\chi_{3234}(29,\cdot)$
• Character field: $\Q(\zeta_{70})$
• Dimension: $5376$
• Sturm bound: $1344$

Defining parameters

Level:	\( N \)	\(=\)	\( 3234 = 2 \cdot 3 \cdot 7^{2} \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	3234.by (of order \(70\) and degree \(24\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 1617 \)
Character field:			\(\Q(\zeta_{70})\)
Sturm bound:			\(1344\)

Dimensions

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

	Total	New	Old
Modular forms	16320	5376	10944
Cusp forms	15936	5376	10560
Eisenstein series	384	0	384

Trace form

5376 * q + 224 * q^4 + 224 * q^16 + 10 * q^22 - 216 * q^25 + 90 * q^27 - 10 * q^28 + 12 * q^31 - 84 * q^33 - 32 * q^34 + 8 * q^37 + 50 * q^40 - 108 * q^42 - 20 * q^45 + 152 * q^49 + 10 * q^55 - 80 * q^57 - 190 * q^58 + 80 * q^61 - 10 * q^63 + 224 * q^64 + 72 * q^66 - 64 * q^67 + 100 * q^69 + 40 * q^72 + 20 * q^73 + 56 * q^75 + 32 * q^78 + 156 * q^81 + 8 * q^82 + 20 * q^84 - 160 * q^85 - 4 * q^88 + 80 * q^90 - 200 * q^91 + 20 * q^93 + 400 * q^94 - 32 * q^97 + 760 * 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

\( S_{2}^{\mathrm{old}}(3234, [\chi]) \simeq \) \(S_{2}^{\mathrm{new}}(1617, [\chi])\)\(^{\oplus 2}\)