Space of modular forms of level 230, weight 6, and Character 230.j

• Label: 230.6.j
• Level: $230$
• Weight: $6$
• Character orbit: 230.j
• Rep. character: $\chi_{230}(9,\cdot)$
• Character field: $\Q(\zeta_{22})$
• Dimension: $600$
• Sturm bound: $216$

Defining parameters

Level:	\( N \)	\(=\)	\( 230 = 2 \cdot 5 \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 6 \)
Character orbit:	\([\chi]\)	\(=\)	230.j (of order \(22\) and degree \(10\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 115 \)
Character field:			\(\Q(\zeta_{22})\)
Sturm bound:			\(216\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{6}(230, [\chi])\).

	Total	New	Old
Modular forms	1840	600	1240
Cusp forms	1760	600	1160
Eisenstein series	80	0	80

Trace form

600 * q + 960 * q^4 - 160 * q^5 + 80 * q^6 + 4232 * q^9 - 168 * q^11 - 2528 * q^14 - 6926 * q^15 - 15360 * q^16 + 4000 * q^19 - 1312 * q^20 + 688 * q^21 - 1280 * q^24 - 14812 * q^25 + 880 * q^26 + 10384 * q^29 + 35856 * q^30 - 23396 * q^31 - 11008 * q^34 - 23824 * q^35 - 67712 * q^36 + 75564 * q^39 - 26340 * q^41 + 2688 * q^44 + 83096 * q^45 - 18432 * q^46 + 171470 * q^49 - 12368 * q^50 + 39848 * q^51 - 191880 * q^54 - 157476 * q^55 + 33408 * q^56 + 146066 * q^59 + 46752 * q^60 - 25320 * q^61 + 245760 * q^64 - 327118 * q^65 + 354816 * q^66 - 998900 * q^69 - 392528 * q^70 + 560368 * q^71 + 35040 * q^74 + 804620 * q^75 - 64000 * q^76 + 408952 * q^79 + 122368 * q^80 + 97364 * q^81 - 188768 * q^84 - 1035158 * q^85 + 464264 * q^86 - 456944 * q^89 - 13536 * q^90 - 1040280 * q^91 + 162624 * q^94 + 1128538 * q^95 + 20480 * q^96 - 1325172 * q^99

Decomposition of \(S_{6}^{\mathrm{new}}(230, [\chi])\) into newform subspaces

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

Decomposition of \(S_{6}^{\mathrm{old}}(230, [\chi])\) into lower level spaces

\( S_{6}^{\mathrm{old}}(230, [\chi]) \simeq \) \(S_{6}^{\mathrm{new}}(115, [\chi])\)\(^{\oplus 2}\)