Space of modular forms of level 245, weight 10, and Character 245.k

• Label: 245.10.k
• Level: $245$
• Weight: $10$
• Character orbit: 245.k
• Rep. character: $\chi_{245}(36,\cdot)$
• Character field: $\Q(\zeta_{7})$
• Dimension: $1008$
• Sturm bound: $280$

Defining parameters

Level:	\( N \)	\(=\)	\( 245 = 5 \cdot 7^{2} \)
Weight:	\( k \)	\(=\)	\( 10 \)
Character orbit:	\([\chi]\)	\(=\)	245.k (of order \(7\) and degree \(6\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 49 \)
Character field:			\(\Q(\zeta_{7})\)
Sturm bound:			\(280\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{10}(245, [\chi])\).

	Total	New	Old
Modular forms	1524	1008	516
Cusp forms	1500	1008	492
Eisenstein series	24	0	24

Trace form

1008 * q - 43008 * q^4 - 1250 * q^5 - 11360 * q^6 - 1140 * q^7 - 1017758 * q^9 - 20000 * q^10 + 56924 * q^11 + 359594 * q^12 - 92620 * q^13 - 2019672 * q^14 - 10472840 * q^16 - 550672 * q^17 - 1193388 * q^18 + 786692 * q^19 - 1865000 * q^20 - 581908 * q^21 - 5673416 * q^22 - 8497860 * q^23 - 22266008 * q^24 - 65625000 * q^25 - 19432612 * q^26 - 3523020 * q^27 - 9249946 * q^28 + 9987894 * q^29 + 4760000 * q^30 + 14419592 * q^31 + 27308120 * q^32 - 47169112 * q^33 - 39195580 * q^34 - 29150000 * q^35 - 266576968 * q^36 - 60257148 * q^37 - 50783092 * q^38 + 31427760 * q^39 - 15360000 * q^40 - 22769184 * q^41 - 260525280 * q^42 - 85520064 * q^43 - 139425720 * q^44 - 45311250 * q^45 - 47814396 * q^46 - 213539280 * q^47 - 205774996 * q^48 + 155970884 * q^49 + 196724360 * q^51 + 217952136 * q^52 - 60488120 * q^53 - 121661748 * q^54 + 4465000 * q^55 + 1695757406 * q^56 - 95935784 * q^57 + 660660476 * q^58 + 163963806 * q^59 - 942331250 * q^60 - 69331800 * q^61 - 945493016 * q^62 + 120484376 * q^63 - 3412088624 * q^64 - 263707500 * q^65 + 2442945614 * q^66 - 468282752 * q^67 + 4520873068 * q^68 + 1501459464 * q^69 + 302030000 * q^70 + 313850824 * q^71 - 1921688076 * q^72 - 924304400 * q^73 - 1467119332 * q^74 + 1168748828 * q^76 - 248610680 * q^77 + 4405147460 * q^78 - 870948960 * q^79 + 2977280000 * q^80 - 9681356566 * q^81 - 4630259458 * q^82 - 4658191508 * q^83 + 4724505550 * q^84 + 230510000 * q^85 + 3292011268 * q^86 + 56279880 * q^87 + 5171234866 * q^88 - 3473803792 * q^89 + 1149502500 * q^90 - 5177331722 * q^91 - 648604726 * q^92 + 1440983208 * q^93 - 7787349194 * q^94 + 466270000 * q^95 - 9324528664 * q^96 + 3660577656 * q^97 - 8338084254 * q^98 + 11860688644 * q^99

Decomposition of \(S_{10}^{\mathrm{new}}(245, [\chi])\) into newform subspaces

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

Decomposition of \(S_{10}^{\mathrm{old}}(245, [\chi])\) into lower level spaces

\( S_{10}^{\mathrm{old}}(245, [\chi]) \simeq \) \(S_{10}^{\mathrm{new}}(49, [\chi])\)\(^{\oplus 2}\)