Space of modular forms of level 615, weight 4, and Character 615.bj

• Label: 615.4.bj
• Level: $615$
• Weight: $4$
• Character orbit: 615.bj
• Rep. character: $\chi_{615}(139,\cdot)$
• Character field: $\Q(\zeta_{10})$
• Dimension: $512$
• Sturm bound: $336$

Defining parameters

Level:	\( N \)	\(=\)	\( 615 = 3 \cdot 5 \cdot 41 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	615.bj (of order \(10\) and degree \(4\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 205 \)
Character field:			\(\Q(\zeta_{10})\)
Sturm bound:			\(336\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{4}(615, [\chi])\).

	Total	New	Old
Modular forms	1024	512	512
Cusp forms	992	512	480
Eisenstein series	32	0	32

Trace form

512 * q + 528 * q^4 - 28 * q^5 - 4608 * q^9 - 154 * q^10 + 56 * q^11 - 248 * q^14 + 36 * q^15 - 2096 * q^16 + 88 * q^19 - 1002 * q^20 - 168 * q^21 - 276 * q^25 - 1408 * q^26 - 712 * q^29 - 456 * q^30 - 568 * q^31 + 336 * q^34 - 1184 * q^35 - 4752 * q^36 + 624 * q^39 + 3660 * q^40 + 816 * q^41 + 2688 * q^44 + 252 * q^45 + 2564 * q^46 + 5976 * q^49 + 852 * q^50 - 1320 * q^51 - 304 * q^55 + 2400 * q^56 - 2388 * q^59 - 36 * q^60 - 2800 * q^61 + 7236 * q^64 + 1542 * q^65 - 3504 * q^66 + 1968 * q^69 - 3764 * q^70 - 216 * q^71 + 7016 * q^74 - 360 * q^75 + 3764 * q^76 - 5456 * q^79 + 4996 * q^80 + 41472 * q^81 + 2124 * q^84 - 8676 * q^85 + 9176 * q^86 + 5248 * q^89 + 1386 * q^90 + 11920 * q^91 + 1752 * q^94 + 3768 * q^95 - 20640 * q^96 - 504 * q^99

Decomposition of \(S_{4}^{\mathrm{new}}(615, [\chi])\) into newform subspaces

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

Decomposition of \(S_{4}^{\mathrm{old}}(615, [\chi])\) into lower level spaces

\( S_{4}^{\mathrm{old}}(615, [\chi]) \simeq \) \(S_{4}^{\mathrm{new}}(205, [\chi])\)\(^{\oplus 2}\)