Space of modular forms of level 325, weight 6, and Character 325.bn

• Label: 325.6.bn
• Level: $325$
• Weight: $6$
• Character orbit: 325.bn
• Rep. character: $\chi_{325}(2,\cdot)$
• Character field: $\Q(\zeta_{60})$
• Dimension: $2768$
• Sturm bound: $210$

Defining parameters

Level:	\( N \)	\(=\)	\( 325 = 5^{2} \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 6 \)
Character orbit:	\([\chi]\)	\(=\)	325.bn (of order \(60\) and degree \(16\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 325 \)
Character field:			\(\Q(\zeta_{60})\)
Sturm bound:			\(210\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{6}(325, [\chi])\).

	Total	New	Old
Modular forms	2832	2832	0
Cusp forms	2768	2768	0
Eisenstein series	64	64	0

Trace form

2768 * q - 26 * q^2 - 8 * q^3 + 5442 * q^4 - 114 * q^5 - 12 * q^6 - 24 * q^7 + 628 * q^8 - 10 * q^9 + 40 * q^10 - 12 * q^11 + 1456 * q^12 - 2242 * q^13 - 40 * q^14 + 568 * q^15 + 85498 * q^16 - 2680 * q^17 + 8760 * q^19 + 10846 * q^20 - 2442 * q^21 + 3074 * q^22 + 7092 * q^23 + 1816 * q^24 - 542 * q^25 - 32 * q^26 - 9164 * q^27 - 10446 * q^28 - 14190 * q^29 - 6824 * q^30 - 12 * q^31 + 72046 * q^32 - 24732 * q^33 + 42052 * q^34 - 59900 * q^35 + 302 * q^36 + 141638 * q^37 - 128 * q^38 - 7180 * q^39 + 27576 * q^40 + 25178 * q^41 + 15526 * q^42 + 12312 * q^43 - 148 * q^44 - 98252 * q^45 - 12 * q^46 + 51030 * q^47 - 146178 * q^48 + 3092488 * q^49 + 387156 * q^50 + 36904 * q^52 + 14210 * q^53 + 68938 * q^54 + 83774 * q^55 + 155764 * q^56 - 232108 * q^57 - 694550 * q^58 - 20 * q^59 + 199872 * q^60 - 6 * q^61 + 137410 * q^62 + 592652 * q^63 - 2604672 * q^64 + 368702 * q^65 - 24 * q^66 + 72038 * q^67 + 320182 * q^68 + 44280 * q^69 + 161358 * q^70 - 12 * q^71 - 165324 * q^72 - 50852 * q^73 - 11400 * q^74 + 55774 * q^75 - 4128 * q^76 - 280488 * q^77 + 383428 * q^78 - 40 * q^79 - 494336 * q^80 + 725880 * q^81 - 1364552 * q^82 - 470350 * q^83 - 100018 * q^84 + 18936 * q^85 - 332 * q^86 + 427848 * q^87 - 2349400 * q^88 - 505420 * q^89 + 8616 * q^90 + 81638 * q^91 - 746272 * q^92 - 100878 * q^93 - 386154 * q^94 + 36456 * q^95 - 518442 * q^96 - 567198 * q^97 - 1262564 * q^98 - 972 * q^99

Decomposition of \(S_{6}^{\mathrm{new}}(325, [\chi])\) into newform subspaces

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