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

• Label: 325.6.n
• Level: $325$
• Weight: $6$
• Character orbit: 325.n
• Rep. character: $\chi_{325}(101,\cdot)$
• Character field: $\Q(\zeta_{6})$
• Dimension: $214$
• Sturm bound: $210$

Defining parameters

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

Dimensions

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

	Total	New	Old
Modular forms	364	226	138
Cusp forms	340	214	126
Eisenstein series	24	12	12

Trace form

214 * q + 3 * q^2 - 8 * q^3 + 1633 * q^4 + 162 * q^6 - 270 * q^7 - 8047 * q^9 - 306 * q^11 + 584 * q^12 + 215 * q^13 - 4052 * q^14 - 21931 * q^16 + 2267 * q^17 + 1722 * q^19 + 1670 * q^22 + 5744 * q^23 + 19494 * q^24 - 833 * q^26 + 18028 * q^27 - 28470 * q^28 + 5331 * q^29 + 12129 * q^32 + 27180 * q^33 + 109335 * q^36 - 10485 * q^37 + 6688 * q^38 - 22954 * q^39 - 38865 * q^41 + 15130 * q^42 + 27098 * q^43 - 88266 * q^46 - 90630 * q^48 + 220069 * q^49 + 57068 * q^51 - 63832 * q^52 - 53014 * q^53 - 139320 * q^54 - 106670 * q^56 - 133569 * q^58 + 71964 * q^59 + 4521 * q^61 - 8346 * q^62 + 372600 * q^63 - 515998 * q^64 + 366640 * q^66 + 130044 * q^67 - 139777 * q^68 + 25434 * q^69 + 185160 * q^71 - 341433 * q^72 - 44317 * q^74 - 267066 * q^76 - 279520 * q^77 + 147454 * q^78 - 555472 * q^79 - 360907 * q^81 + 107091 * q^82 - 432444 * q^84 - 8604 * q^87 - 202390 * q^88 + 365238 * q^89 - 230246 * q^91 + 1467728 * q^92 + 445272 * q^93 + 286020 * q^94 - 41112 * q^97 + 236829 * q^98

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

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

Decomposition of $S_{6}^{\mathrm{old}}(325, [\chi])$ into lower level spaces

$S_{6}^{\mathrm{old}}(325, [\chi]) \simeq$ $S_{6}^{\mathrm{new}}(13, [\chi])$$^{\oplus 3}$$\oplus$$S_{6}^{\mathrm{new}}(65, [\chi])$$^{\oplus 2}$