Space of modular forms of level 322, weight 4, and Character 322.m

• Label: 322.4.m
• Level: $322$
• Weight: $4$
• Character orbit: 322.m
• Rep. character: $\chi_{322}(9,\cdot)$
• Character field: $\Q(\zeta_{33})$
• Dimension: $960$
• Sturm bound: $192$

Defining parameters

Level:	\( N \)	\(=\)	\( 322 = 2 \cdot 7 \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	322.m (of order \(33\) and degree \(20\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 161 \)
Character field:			\(\Q(\zeta_{33})\)
Sturm bound:			\(192\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{4}(322, [\chi])\).

	Total	New	Old
Modular forms	2960	960	2000
Cusp forms	2800	960	1840
Eisenstein series	160	0	160

Trace form

960 * q + 192 * q^4 - 4 * q^5 - 16 * q^6 + 8 * q^7 + 404 * q^9 - 40 * q^10 - 28 * q^11 - 168 * q^14 + 176 * q^15 + 768 * q^16 + 120 * q^17 + 184 * q^18 - 144 * q^19 + 736 * q^20 - 2612 * q^21 + 288 * q^22 + 1030 * q^23 + 32 * q^24 + 1480 * q^25 - 232 * q^26 + 216 * q^27 + 288 * q^28 - 104 * q^29 - 1456 * q^30 + 88 * q^31 - 128 * q^33 + 64 * q^34 - 1346 * q^35 - 3232 * q^36 - 804 * q^37 - 280 * q^38 + 908 * q^39 - 160 * q^40 + 1360 * q^41 + 248 * q^42 - 5208 * q^43 - 112 * q^44 + 5900 * q^45 + 152 * q^46 - 356 * q^47 + 2830 * q^49 - 1280 * q^50 - 428 * q^51 - 888 * q^53 - 5016 * q^54 + 232 * q^55 - 1648 * q^56 + 5896 * q^57 + 1560 * q^58 - 4508 * q^59 - 352 * q^60 + 304 * q^61 - 1392 * q^62 + 5152 * q^63 - 6144 * q^64 - 6008 * q^65 + 1024 * q^66 + 1272 * q^67 + 6464 * q^68 - 428 * q^69 + 6184 * q^70 - 1216 * q^71 - 2080 * q^72 + 264 * q^73 - 1568 * q^74 + 8360 * q^75 + 1152 * q^76 - 4100 * q^77 - 4576 * q^78 + 4192 * q^79 - 64 * q^80 + 2892 * q^81 - 7920 * q^82 + 1280 * q^83 - 4008 * q^84 + 436 * q^85 + 4116 * q^86 - 1242 * q^87 - 576 * q^88 + 340 * q^89 - 528 * q^90 - 6176 * q^91 - 496 * q^92 - 584 * q^93 + 3960 * q^94 + 12360 * q^95 + 128 * q^96 + 9832 * q^97 - 1656 * q^98 - 18620 * q^99

Decomposition of \(S_{4}^{\mathrm{new}}(322, [\chi])\) into newform subspaces

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

Decomposition of \(S_{4}^{\mathrm{old}}(322, [\chi])\) into lower level spaces

\( S_{4}^{\mathrm{old}}(322, [\chi]) \simeq \) \(S_{4}^{\mathrm{new}}(161, [\chi])\)\(^{\oplus 2}\)