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

• Label: 322.4.i
• Level: $322$
• Weight: $4$
• Character orbit: 322.i
• Rep. character: $\chi_{322}(29,\cdot)$
• Character field: $\Q(\zeta_{11})$
• Dimension: $360$
• Sturm bound: $192$

Defining parameters

Level:	\( N \)	\(=\)	\( 322 = 2 \cdot 7 \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	322.i (of order \(11\) and degree \(10\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 23 \)
Character field:			\(\Q(\zeta_{11})\)
Sturm bound:			\(192\)

Dimensions

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

	Total	New	Old
Modular forms	1480	360	1120
Cusp forms	1400	360	1040
Eisenstein series	80	0	80

Trace form

360 * q - 16 * q^3 - 144 * q^4 + 32 * q^5 - 196 * q^9 - 124 * q^11 - 64 * q^12 - 224 * q^13 - 56 * q^14 - 1400 * q^15 - 576 * q^16 - 416 * q^17 + 72 * q^18 + 456 * q^19 + 128 * q^20 - 84 * q^21 + 736 * q^22 + 1200 * q^23 - 588 * q^25 + 360 * q^26 - 760 * q^27 - 1232 * q^29 - 1416 * q^30 - 2336 * q^31 - 2592 * q^33 - 288 * q^34 + 112 * q^35 - 784 * q^36 - 480 * q^37 - 64 * q^38 - 272 * q^39 + 516 * q^41 - 168 * q^42 + 2784 * q^43 - 496 * q^44 + 888 * q^45 + 200 * q^46 + 5800 * q^47 - 256 * q^48 - 1764 * q^49 + 480 * q^50 - 732 * q^51 - 896 * q^52 - 400 * q^53 - 1200 * q^54 - 10640 * q^55 - 224 * q^56 - 12420 * q^57 - 128 * q^58 - 1848 * q^59 + 208 * q^60 - 1552 * q^61 + 3128 * q^62 + 840 * q^63 - 2304 * q^64 - 1080 * q^65 + 9696 * q^66 + 8412 * q^67 - 256 * q^68 + 15616 * q^69 + 1008 * q^70 + 11760 * q^71 - 64 * q^72 + 2792 * q^73 + 3992 * q^74 - 11756 * q^75 + 64 * q^76 - 2904 * q^78 - 1476 * q^79 - 2304 * q^80 - 14000 * q^81 + 784 * q^82 - 14884 * q^83 - 336 * q^84 - 15120 * q^85 + 520 * q^86 - 2504 * q^87 - 928 * q^88 + 6172 * q^89 - 3680 * q^90 + 4480 * q^91 + 928 * q^92 + 4160 * q^93 + 2592 * q^94 + 6580 * q^95 - 24108 * q^97 + 692 * 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

\( S_{4}^{\mathrm{old}}(322, [\chi]) \simeq \) \(S_{4}^{\mathrm{new}}(23, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(46, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(161, [\chi])\)\(^{\oplus 2}\)