Space of modular forms of level 483, weight 4, and Character 483.q

• Label: 483.4.q
• Level: $483$
• Weight: $4$
• Character orbit: 483.q
• Rep. character: $\chi_{483}(64,\cdot)$
• Character field: $\Q(\zeta_{11})$
• Dimension: $720$
• Sturm bound: $256$

Defining parameters

Level:	\( N \)	\(=\)	\( 483 = 3 \cdot 7 \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	483.q (of order \(11\) and degree \(10\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 23 \)
Character field:			\(\Q(\zeta_{11})\)
Sturm bound:			\(256\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{4}(483, [\chi])\).

	Total	New	Old
Modular forms	1960	720	1240
Cusp forms	1880	720	1160
Eisenstein series	80	0	80

Trace form

720 * q - 4 * q^2 - 292 * q^4 + 24 * q^6 - 28 * q^7 + 36 * q^8 - 648 * q^9 + 120 * q^10 - 40 * q^11 - 128 * q^13 + 140 * q^14 - 168 * q^15 - 1860 * q^16 - 416 * q^17 - 36 * q^18 + 360 * q^19 - 760 * q^20 - 84 * q^21 + 1344 * q^22 + 1004 * q^23 + 648 * q^24 - 1104 * q^25 + 680 * q^26 - 140 * q^28 - 1152 * q^29 - 192 * q^30 - 1624 * q^31 - 1668 * q^32 + 384 * q^33 - 3684 * q^34 + 112 * q^35 - 3618 * q^36 - 932 * q^37 - 128 * q^38 + 216 * q^39 + 3140 * q^40 + 2440 * q^41 - 168 * q^42 + 2452 * q^43 + 4958 * q^44 + 7496 * q^46 + 7328 * q^47 + 5616 * q^48 - 3528 * q^49 + 5446 * q^50 + 1212 * q^51 - 2912 * q^52 + 1432 * q^53 - 972 * q^54 - 8896 * q^55 + 924 * q^56 - 3588 * q^57 - 1058 * q^58 + 112 * q^59 - 7668 * q^60 - 3376 * q^61 + 1992 * q^62 - 252 * q^63 + 3508 * q^64 + 192 * q^65 + 1248 * q^66 + 2328 * q^67 - 3088 * q^68 - 144 * q^69 + 1008 * q^70 + 1832 * q^71 + 324 * q^72 + 2784 * q^73 - 8426 * q^74 - 1056 * q^75 - 26004 * q^76 - 8568 * q^77 + 528 * q^78 - 7840 * q^79 - 15920 * q^80 - 5832 * q^81 - 4344 * q^82 - 976 * q^83 - 1008 * q^84 - 8016 * q^85 + 26056 * q^86 + 1776 * q^87 - 1198 * q^88 + 20472 * q^89 + 1080 * q^90 + 15400 * q^91 + 3192 * q^92 - 744 * q^93 - 568 * q^94 + 9808 * q^95 - 19056 * q^96 + 10488 * q^97 + 882 * q^98 - 360 * q^99

Decomposition of \(S_{4}^{\mathrm{new}}(483, [\chi])\) into newform subspaces

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

Decomposition of \(S_{4}^{\mathrm{old}}(483, [\chi])\) into lower level spaces

\( S_{4}^{\mathrm{old}}(483, [\chi]) \simeq \) \(S_{4}^{\mathrm{new}}(23, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(69, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(161, [\chi])\)\(^{\oplus 2}\)