Space of modular forms of level 414, weight 4, and Character 414.e

• Label: 414.4.e
• Level: $414$
• Weight: $4$
• Character orbit: 414.e
• Rep. character: $\chi_{414}(139,\cdot)$
• Character field: $\Q(\zeta_{3})$
• Dimension: $132$
• Sturm bound: $288$

Defining parameters

Level:	\( N \)	\(=\)	\( 414 = 2 \cdot 3^{2} \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	414.e (of order \(3\) and degree \(2\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 9 \)
Character field:			\(\Q(\zeta_{3})\)
Sturm bound:			\(288\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{4}(414, [\chi])\).

	Total	New	Old
Modular forms	440	132	308
Cusp forms	424	132	292
Eisenstein series	16	0	16

Trace form

132 * q - 4 * q^2 + 2 * q^3 - 264 * q^4 + 20 * q^6 - 24 * q^7 + 32 * q^8 + 118 * q^9 - 34 * q^11 - 16 * q^12 + 48 * q^13 - 88 * q^15 - 1056 * q^16 - 116 * q^17 - 184 * q^18 - 420 * q^19 + 128 * q^21 + 36 * q^22 + 80 * q^24 - 1650 * q^25 + 624 * q^26 - 304 * q^27 + 192 * q^28 + 484 * q^29 + 24 * q^30 - 60 * q^31 - 64 * q^32 - 594 * q^33 - 180 * q^34 - 2664 * q^35 - 296 * q^36 - 672 * q^37 - 188 * q^38 + 1584 * q^39 - 646 * q^41 + 1480 * q^42 - 258 * q^43 + 272 * q^44 + 1832 * q^45 + 760 * q^47 + 32 * q^48 - 2754 * q^49 - 476 * q^50 + 2722 * q^51 + 192 * q^52 - 2240 * q^53 - 1636 * q^54 + 1224 * q^55 - 3206 * q^57 - 504 * q^58 - 386 * q^59 + 1664 * q^60 - 1680 * q^61 + 3952 * q^62 - 348 * q^63 + 8448 * q^64 - 1588 * q^65 + 2496 * q^66 - 1950 * q^67 + 232 * q^68 - 72 * q^70 + 3744 * q^71 + 368 * q^72 + 516 * q^73 - 6710 * q^75 + 840 * q^76 - 1216 * q^77 + 3560 * q^78 + 2964 * q^79 - 2474 * q^81 + 5832 * q^82 + 2148 * q^83 - 1600 * q^84 - 216 * q^85 - 12 * q^86 + 2776 * q^87 + 144 * q^88 + 360 * q^89 + 3688 * q^90 - 5016 * q^91 + 564 * q^93 + 1716 * q^95 - 640 * q^96 + 246 * q^97 + 5000 * q^98 - 384 * q^99

Decomposition of \(S_{4}^{\mathrm{new}}(414, [\chi])\) into newform subspaces

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

Decomposition of \(S_{4}^{\mathrm{old}}(414, [\chi])\) into lower level spaces

\( S_{4}^{\mathrm{old}}(414, [\chi]) \simeq \) \(S_{4}^{\mathrm{new}}(9, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(18, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(207, [\chi])\)\(^{\oplus 2}\)