Space of modular forms of level 1058, weight 4, and Character 1058.c

• Label: 1058.4.c
• Level: $1058$
• Weight: $4$
• Character orbit: 1058.c
• Rep. character: $\chi_{1058}(177,\cdot)$
• Character field: $\Q(\zeta_{11})$
• Dimension: $1260$
• Sturm bound: $552$

Defining parameters

Level:	\( N \)	\(=\)	\( 1058 = 2 \cdot 23^{2} \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	1058.c (of order \(11\) and degree \(10\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 23 \)
Character field:			\(\Q(\zeta_{11})\)
Sturm bound:			\(552\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{4}(1058, [\chi])\).

	Total	New	Old
Modular forms	4380	1260	3120
Cusp forms	3900	1260	2640
Eisenstein series	480	0	480

Trace form

1260 * q - 8 * q^3 - 504 * q^4 - 10 * q^5 - 8 * q^6 + 8 * q^7 - 1042 * q^9 - 20 * q^10 - 34 * q^11 - 32 * q^12 - 112 * q^13 + 40 * q^14 - 744 * q^15 - 2016 * q^16 - 148 * q^17 - 40 * q^18 + 258 * q^19 + 312 * q^20 + 1060 * q^21 + 296 * q^22 - 32 * q^24 - 2518 * q^25 + 412 * q^26 - 272 * q^27 - 144 * q^28 - 828 * q^29 - 1016 * q^30 - 1344 * q^31 - 988 * q^33 - 520 * q^34 - 926 * q^35 - 4168 * q^36 - 894 * q^37 - 436 * q^38 - 312 * q^39 - 80 * q^40 + 1066 * q^41 - 64 * q^42 + 1350 * q^43 - 136 * q^44 + 2644 * q^45 + 4976 * q^47 - 128 * q^48 - 5316 * q^49 + 592 * q^50 - 328 * q^51 - 448 * q^52 + 448 * q^53 - 3252 * q^54 - 5640 * q^55 - 1776 * q^56 - 9364 * q^57 - 1552 * q^58 - 3566 * q^59 - 72 * q^60 + 414 * q^61 + 876 * q^62 + 4600 * q^63 - 8064 * q^64 + 6368 * q^65 + 5360 * q^66 + 3330 * q^67 + 3104 * q^68 + 11248 * q^70 + 6020 * q^71 + 1952 * q^72 + 676 * q^73 + 3564 * q^74 - 5594 * q^75 + 152 * q^76 - 1312 * q^77 - 1148 * q^78 - 3178 * q^79 - 1568 * q^80 - 15714 * q^81 - 3752 * q^82 - 6808 * q^83 - 4824 * q^84 - 5870 * q^85 - 3856 * q^86 + 1482 * q^87 - 752 * q^88 + 826 * q^89 - 4804 * q^90 + 2048 * q^91 + 3804 * q^93 + 1056 * q^94 + 452 * q^95 - 128 * q^96 - 11758 * q^97 - 6120 * q^98 - 8964 * q^99

Decomposition of \(S_{4}^{\mathrm{new}}(1058, [\chi])\) into newform subspaces

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

Decomposition of \(S_{4}^{\mathrm{old}}(1058, [\chi])\) into lower level spaces

\( S_{4}^{\mathrm{old}}(1058, [\chi]) \simeq \) \(S_{4}^{\mathrm{new}}(23, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(46, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(529, [\chi])\)\(^{\oplus 2}\)