Space of modular forms of level 546, weight 4, and Character 546.j

• Label: 546.4.j
• Level: $546$
• Weight: $4$
• Character orbit: 546.j
• Rep. character: $\chi_{546}(289,\cdot)$
• Character field: $\Q(\zeta_{3})$
• Dimension: $112$
• Sturm bound: $448$

Defining parameters

Level:	\( N \)	\(=\)	\( 546 = 2 \cdot 3 \cdot 7 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	546.j (of order \(3\) and degree \(2\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 91 \)
Character field:			\(\Q(\zeta_{3})\)
Sturm bound:			\(448\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{4}(546, [\chi])\).

	Total	New	Old
Modular forms	688	112	576
Cusp forms	656	112	544
Eisenstein series	32	0	32

Trace form

112 * q + 448 * q^4 + 10 * q^7 - 504 * q^9 - 80 * q^10 - 28 * q^11 + 70 * q^13 - 48 * q^14 + 1792 * q^16 - 8 * q^17 - 116 * q^19 + 156 * q^21 - 56 * q^22 + 352 * q^23 - 1528 * q^25 - 152 * q^26 + 40 * q^28 - 172 * q^29 + 386 * q^31 + 148 * q^35 - 2016 * q^36 - 1960 * q^37 - 248 * q^38 + 294 * q^39 - 320 * q^40 + 104 * q^41 + 474 * q^43 - 112 * q^44 + 1328 * q^46 - 48 * q^47 + 910 * q^49 + 736 * q^50 + 396 * q^51 + 280 * q^52 + 1332 * q^53 + 552 * q^55 - 192 * q^56 + 168 * q^57 + 400 * q^58 - 4384 * q^59 - 2784 * q^61 + 376 * q^62 - 18 * q^63 + 7168 * q^64 - 3028 * q^65 - 1056 * q^66 + 2910 * q^67 - 32 * q^68 - 1200 * q^69 + 2592 * q^70 - 2312 * q^71 - 94 * q^73 - 624 * q^74 + 624 * q^75 - 464 * q^76 - 3296 * q^77 - 192 * q^78 + 2358 * q^79 - 4536 * q^81 - 1456 * q^82 + 4528 * q^83 + 624 * q^84 + 3800 * q^85 + 1288 * q^86 + 1872 * q^87 - 224 * q^88 + 4528 * q^89 + 1440 * q^90 + 588 * q^91 + 1408 * q^92 - 3780 * q^93 - 4192 * q^94 + 4144 * q^95 + 3008 * q^97 + 1584 * q^98 + 504 * q^99

Decomposition of \(S_{4}^{\mathrm{new}}(546, [\chi])\) into newform subspaces

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

Decomposition of \(S_{4}^{\mathrm{old}}(546, [\chi])\) into lower level spaces

\( S_{4}^{\mathrm{old}}(546, [\chi]) \simeq \) \(S_{4}^{\mathrm{new}}(91, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(182, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(273, [\chi])\)\(^{\oplus 2}\)