Space of modular forms of level 3549, weight 2, and Character 3549.eb

• Label: 3549.2.eb
• Level: $3549$
• Weight: $2$
• Character orbit: 3549.eb
• Rep. character: $\chi_{3549}(115,\cdot)$
• Character field: $\Q(\zeta_{156})$
• Dimension: $11664$
• Sturm bound: $970$

Defining parameters

Level:	\( N \)	\(=\)	\( 3549 = 3 \cdot 7 \cdot 13^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	3549.eb (of order \(156\) and degree \(48\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 1183 \)
Character field:			\(\Q(\zeta_{156})\)
Sturm bound:			\(970\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(3549, [\chi])\).

	Total	New	Old
Modular forms	23472	11664	11808
Cusp forms	23088	11664	11424
Eisenstein series	384	0	384

Trace form

11664 * q + 4 * q^7 + 972 * q^9 - 8 * q^11 + 8 * q^12 - 32 * q^14 - 492 * q^16 + 10 * q^19 - 2 * q^21 + 60 * q^26 - 4 * q^28 - 8 * q^31 + 240 * q^32 - 16 * q^35 - 16 * q^37 - 16 * q^39 + 60 * q^40 + 36 * q^41 - 24 * q^42 + 36 * q^43 + 64 * q^44 + 52 * q^46 + 14 * q^49 + 40 * q^50 - 24 * q^51 - 100 * q^52 + 36 * q^55 - 36 * q^56 + 38 * q^57 + 72 * q^58 + 44 * q^60 - 72 * q^62 - 4 * q^63 - 56 * q^65 + 398 * q^67 - 264 * q^70 - 36 * q^71 + 38 * q^73 - 792 * q^74 - 14 * q^75 + 76 * q^76 + 8 * q^78 - 96 * q^80 - 972 * q^81 - 96 * q^82 - 48 * q^83 - 72 * q^84 - 420 * q^85 - 576 * q^86 - 36 * q^87 - 48 * q^89 - 26 * q^91 - 72 * q^92 + 14 * q^93 + 468 * q^94 - 48 * q^95 - 12 * q^96 - 838 * q^97 + 72 * q^98 + 8 * q^99

Decomposition of \(S_{2}^{\mathrm{new}}(3549, [\chi])\) into newform subspaces

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

Decomposition of \(S_{2}^{\mathrm{old}}(3549, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(3549, [\chi]) \simeq \) \(S_{2}^{\mathrm{new}}(1183, [\chi])\)\(^{\oplus 2}\)