Space of modular forms of level 980, weight 3, and Character 980.bo

• Label: 980.3.bo
• Level: $980$
• Weight: $3$
• Character orbit: 980.bo
• Rep. character: $\chi_{980}(61,\cdot)$
• Character field: $\Q(\zeta_{42})$
• Dimension: $456$
• Sturm bound: $504$

Defining parameters

Level:	\( N \)	\(=\)	\( 980 = 2^{2} \cdot 5 \cdot 7^{2} \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	980.bo (of order \(42\) and degree \(12\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 49 \)
Character field:			\(\Q(\zeta_{42})\)
Sturm bound:			\(504\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{3}(980, [\chi])\).

	Total	New	Old
Modular forms	4104	456	3648
Cusp forms	3960	456	3504
Eisenstein series	144	0	144

Trace form

456 * q + 6 * q^3 - 14 * q^7 - 184 * q^9 - 4 * q^11 + 48 * q^17 + 6 * q^19 - 28 * q^21 - 144 * q^23 - 190 * q^25 + 210 * q^27 + 120 * q^29 + 60 * q^31 - 192 * q^33 - 130 * q^35 - 330 * q^37 + 96 * q^39 - 196 * q^41 + 196 * q^43 - 60 * q^45 - 332 * q^47 + 256 * q^49 + 222 * q^51 + 348 * q^53 - 224 * q^57 + 528 * q^59 - 142 * q^61 + 446 * q^63 + 20 * q^65 + 74 * q^67 - 112 * q^69 - 152 * q^71 - 78 * q^73 + 30 * q^75 - 30 * q^77 - 146 * q^79 + 2118 * q^81 - 210 * q^83 - 60 * q^85 + 1574 * q^87 + 890 * q^89 + 796 * q^91 + 68 * q^93 - 20 * q^95 + 428 * q^99

Decomposition of \(S_{3}^{\mathrm{new}}(980, [\chi])\) into newform subspaces

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

Decomposition of \(S_{3}^{\mathrm{old}}(980, [\chi])\) into lower level spaces

\( S_{3}^{\mathrm{old}}(980, [\chi]) \simeq \) \(S_{3}^{\mathrm{new}}(49, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(98, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(196, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(245, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(490, [\chi])\)\(^{\oplus 2}\)