Space of modular forms of level 1014, weight 4, and Character 1014.q

• Label: 1014.4.q
• Level: $1014$
• Weight: $4$
• Character orbit: 1014.q
• Rep. character: $\chi_{1014}(55,\cdot)$
• Character field: $\Q(\zeta_{39})$
• Dimension: $2208$
• Sturm bound: $728$

Defining parameters

Level:	\( N \)	\(=\)	\( 1014 = 2 \cdot 3 \cdot 13^{2} \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	1014.q (of order \(39\) and degree \(24\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 169 \)
Character field:			\(\Q(\zeta_{39})\)
Sturm bound:			\(728\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{4}(1014, [\chi])\).

	Total	New	Old
Modular forms	13200	2208	10992
Cusp forms	13008	2208	10800
Eisenstein series	192	0	192

Trace form

2208 * q - 4 * q^2 + 6 * q^3 + 368 * q^4 - 20 * q^5 + 26 * q^7 + 32 * q^8 + 828 * q^9 + 60 * q^10 - 68 * q^11 - 48 * q^12 - 82 * q^13 - 16 * q^14 - 24 * q^15 + 1472 * q^16 + 66 * q^17 + 72 * q^18 - 104 * q^19 + 40 * q^20 + 252 * q^21 - 1056 * q^22 + 28 * q^23 - 5092 * q^25 + 380 * q^26 - 108 * q^27 + 104 * q^28 + 6 * q^29 + 120 * q^30 - 1272 * q^31 - 64 * q^32 + 192 * q^33 - 440 * q^34 - 148 * q^35 + 3312 * q^36 + 550 * q^37 - 208 * q^38 + 96 * q^39 + 560 * q^40 - 362 * q^41 + 168 * q^42 + 90 * q^43 + 544 * q^44 + 90 * q^45 - 832 * q^46 - 968 * q^47 + 96 * q^48 + 4318 * q^49 - 768 * q^50 - 288 * q^51 + 648 * q^52 + 1014 * q^53 + 2772 * q^55 + 32 * q^56 - 504 * q^57 + 548 * q^58 - 556 * q^59 - 1056 * q^60 - 188 * q^61 - 696 * q^62 + 234 * q^63 - 11776 * q^64 - 2606 * q^65 - 1680 * q^66 - 6306 * q^67 + 264 * q^68 + 1176 * q^69 - 10944 * q^70 + 22796 * q^71 - 144 * q^72 + 376 * q^73 + 12544 * q^74 + 738 * q^75 + 3120 * q^76 + 6872 * q^77 + 864 * q^78 + 500 * q^79 + 160 * q^80 + 7452 * q^81 + 676 * q^82 - 2928 * q^83 - 504 * q^84 + 9832 * q^85 - 1752 * q^86 + 2256 * q^87 + 352 * q^88 - 2756 * q^89 - 1080 * q^90 - 7106 * q^91 - 224 * q^92 - 7266 * q^93 + 10312 * q^94 - 14752 * q^95 + 7794 * q^97 - 3348 * q^98 + 1224 * q^99

Decomposition of \(S_{4}^{\mathrm{new}}(1014, [\chi])\) into newform subspaces

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

Decomposition of \(S_{4}^{\mathrm{old}}(1014, [\chi])\) into lower level spaces

\( S_{4}^{\mathrm{old}}(1014, [\chi]) \simeq \) \(S_{4}^{\mathrm{new}}(169, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(338, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(507, [\chi])\)\(^{\oplus 2}\)