Space of modular forms of level 325, weight 10, and Character 325.bn

• Label: 325.10.bn
• Level: $325$
• Weight: $10$
• Character orbit: 325.bn
• Rep. character: $\chi_{325}(2,\cdot)$
• Character field: $\Q(\zeta_{60})$
• Dimension: $5008$
• Sturm bound: $350$

Defining parameters

Level:	$N$	$=$	$325 = 5^{2} \cdot 13$
Weight:	$k$	$=$	$10$
Character orbit:	$[\chi]$	$=$	325.bn (of order $60$ and degree $16$)
Character conductor:	$\operatorname{cond}(\chi)$	$=$	$325$
Character field:			$\Q(\zeta_{60})$
Sturm bound:			$350$

Dimensions

The following table gives the dimensions of various subspaces of $M_{10}(325, [\chi])$.

	Total	New	Old
Modular forms	5072	5072	0
Cusp forms	5008	5008	0
Eisenstein series	64	64	0

Trace form

5008 * q + 14 * q^2 - 8 * q^3 + 159202 * q^4 + 106 * q^5 - 12 * q^6 - 24 * q^7 - 51212 * q^8 - 10 * q^9 + 1000 * q^10 - 12 * q^11 + 229936 * q^12 + 150938 * q^13 - 40 * q^14 - 1456532 * q^15 + 40239098 * q^16 - 1189340 * q^17 - 2248940 * q^19 - 2493954 * q^20 - 196842 * q^21 + 1658274 * q^22 - 2148088 * q^23 + 155416 * q^24 - 6091702 * q^25 - 32 * q^26 + 2304916 * q^27 - 2624526 * q^28 - 5736890 * q^29 + 804136 * q^30 - 12 * q^31 - 71028434 * q^32 - 29346642 * q^33 - 67719028 * q^34 - 48417260 * q^35 + 5102 * q^36 + 96345578 * q^37 - 2048 * q^38 - 74222380 * q^39 + 159487416 * q^40 + 199720318 * q^41 - 51897194 * q^42 - 92584168 * q^43 - 2068 * q^44 + 321355528 * q^45 - 12 * q^46 - 100686720 * q^47 - 328940418 * q^48 + 13881640808 * q^49 + 826739396 * q^50 - 529985816 * q^52 + 39224550 * q^53 + 1175573098 * q^54 + 6668404 * q^55 + 400390324 * q^56 - 361373188 * q^57 - 1665619430 * q^58 - 20 * q^59 - 1350858048 * q^60 - 6 * q^61 + 395851810 * q^62 - 3435112618 * q^63 - 20065544192 * q^64 + 1280444132 * q^65 - 24 * q^66 + 235770638 * q^67 + 134412502 * q^68 - 4616220870 * q^69 - 1147125522 * q^70 - 12 * q^71 + 111598356 * q^72 - 280784772 * q^73 + 998184480 * q^74 + 2242278364 * q^75 - 1048608 * q^76 - 259446408 * q^77 - 6323162492 * q^78 - 40 * q^79 + 242602624 * q^80 - 35921811840 * q^81 - 3857018552 * q^82 - 240010000 * q^83 - 242044978 * q^84 + 2871975416 * q^85 - 5132 * q^86 - 2734303332 * q^87 + 19861441320 * q^88 + 2125759790 * q^89 - 1907934144 * q^90 - 6613045762 * q^91 + 2958520288 * q^92 + 3925180722 * q^93 + 9059870486 * q^94 - 3435408264 * q^95 + 68386998 * q^96 + 1470446302 * q^97 - 3860353004 * q^98 - 78732 * q^99

Decomposition of $S_{10}^{\mathrm{new}}(325, [\chi])$ into newform subspaces

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