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

• Label: 3234.2.bg
• Level: $3234$
• Weight: $2$
• Character orbit: 3234.bg
• Rep. character: $\chi_{3234}(361,\cdot)$
• Character field: $\Q(\zeta_{15})$
• Dimension: $640$
• Sturm bound: $1344$

Defining parameters

Level:	\( N \)	\(=\)	\( 3234 = 2 \cdot 3 \cdot 7^{2} \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	3234.bg (of order \(15\) and degree \(8\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 77 \)
Character field:			\(\Q(\zeta_{15})\)
Sturm bound:			\(1344\)

Dimensions

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

	Total	New	Old
Modular forms	5632	640	4992
Cusp forms	5120	640	4480
Eisenstein series	512	0	512

Trace form

640 * q + 80 * q^4 - 8 * q^5 - 8 * q^6 + 80 * q^9 - 36 * q^10 - 8 * q^11 - 16 * q^13 - 12 * q^15 + 80 * q^16 - 12 * q^17 + 16 * q^20 - 4 * q^22 - 8 * q^23 + 4 * q^24 + 44 * q^25 - 8 * q^26 - 24 * q^29 + 16 * q^30 + 6 * q^31 - 2 * q^33 - 32 * q^34 - 160 * q^36 - 12 * q^37 - 8 * q^38 + 14 * q^40 + 24 * q^41 + 16 * q^43 + 12 * q^44 - 8 * q^45 + 8 * q^46 - 88 * q^47 + 24 * q^51 + 8 * q^52 - 16 * q^53 - 16 * q^54 - 12 * q^55 - 32 * q^57 + 2 * q^58 + 32 * q^59 - 4 * q^60 - 20 * q^61 + 96 * q^62 - 160 * q^64 + 128 * q^65 + 128 * q^67 - 12 * q^68 + 40 * q^69 + 240 * q^71 + 32 * q^73 + 16 * q^74 - 8 * q^75 + 80 * q^76 + 16 * q^79 + 12 * q^80 + 80 * q^81 + 24 * q^82 + 208 * q^83 + 200 * q^85 + 36 * q^86 - 4 * q^87 + 22 * q^88 + 80 * q^89 - 8 * q^90 + 16 * q^92 - 40 * q^93 + 56 * q^94 + 44 * q^95 + 4 * q^96 + 24 * q^97 + 16 * 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

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