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

• Label: 245.10.e
• Level: $245$
• Weight: $10$
• Character orbit: 245.e
• Rep. character: $\chi_{245}(116,\cdot)$
• Character field: $\Q(\zeta_{3})$
• Dimension: $240$
• Sturm bound: $280$

Defining parameters

Level:	\( N \)	\(=\)	\( 245 = 5 \cdot 7^{2} \)
Weight:	\( k \)	\(=\)	\( 10 \)
Character orbit:	\([\chi]\)	\(=\)	245.e (of order \(3\) and degree \(2\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 7 \)
Character field:			\(\Q(\zeta_{3})\)
Sturm bound:			\(280\)

Dimensions

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

	Total	New	Old
Modular forms	520	240	280
Cusp forms	488	240	248
Eisenstein series	32	0	32

Trace form

240 * q - 68 * q^2 + 324 * q^3 - 30380 * q^4 + 1250 * q^5 - 4544 * q^6 + 135864 * q^8 - 802522 * q^9 + 20000 * q^10 + 129358 * q^11 + 193502 * q^12 - 639344 * q^13 - 530000 * q^15 - 6855536 * q^16 + 726916 * q^17 - 2827434 * q^18 - 500174 * q^19 - 1015000 * q^20 - 1668168 * q^22 - 1766404 * q^23 + 11734856 * q^24 - 46875000 * q^25 - 1855086 * q^26 - 18415320 * q^27 + 21837092 * q^29 + 2380000 * q^30 + 9552424 * q^31 - 5870032 * q^32 + 15576640 * q^33 - 71723608 * q^34 + 452572160 * q^36 + 12240460 * q^37 + 92967488 * q^38 - 49012216 * q^39 + 15360000 * q^40 + 25959632 * q^41 + 44210168 * q^43 + 203503670 * q^44 + 14250000 * q^45 - 215307206 * q^46 + 120782752 * q^47 - 513498212 * q^48 + 53125000 * q^50 + 166961464 * q^51 + 217058244 * q^52 + 199430060 * q^53 + 60156 * q^54 - 224080000 * q^55 + 768437256 * q^57 - 191757658 * q^58 - 46816604 * q^59 + 459826250 * q^60 - 345410298 * q^61 + 118990680 * q^62 + 2799350568 * q^64 - 178013750 * q^65 - 1232991676 * q^66 - 715948492 * q^67 + 545621672 * q^68 + 2753035692 * q^69 - 2371129232 * q^71 - 1889109850 * q^72 - 751678348 * q^73 + 190452894 * q^74 + 126562500 * q^75 + 2859908284 * q^76 - 395465360 * q^78 - 1573697620 * q^79 + 341760000 * q^80 - 4838331396 * q^81 + 322489250 * q^82 + 1277519840 * q^83 + 789550000 * q^85 - 5238078108 * q^86 + 1348411348 * q^87 - 1164785144 * q^88 + 355814886 * q^89 - 3117802500 * q^90 - 5308345460 * q^92 + 504018924 * q^93 - 1801884670 * q^94 + 335740000 * q^95 - 1214975308 * q^96 - 8287090288 * q^97 - 2236478452 * 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

\( S_{10}^{\mathrm{old}}(245, [\chi]) \simeq \) \(S_{10}^{\mathrm{new}}(7, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{10}^{\mathrm{new}}(35, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{10}^{\mathrm{new}}(49, [\chi])\)\(^{\oplus 2}\)