Space of modular forms of level 3950, weight 2, and Character 3950.bo

• Label: 3950.2.bo
• Level: $3950$
• Weight: $2$
• Character orbit: 3950.bo
• Rep. character: $\chi_{3950}(11,\cdot)$
• Character field: $\Q(\zeta_{195})$
• Dimension: $19200$
• Sturm bound: $1200$

Defining parameters

Level:	$N$	$=$	$3950 = 2 \cdot 5^{2} \cdot 79$
Weight:	$k$	$=$	$2$
Character orbit:	$[\chi]$	$=$	3950.bo (of order $195$ and degree $96$)
Character conductor:	$\operatorname{cond}(\chi)$	$=$	$1975$
Character field:			$\Q(\zeta_{195})$
Sturm bound:			$1200$

Dimensions

The following table gives the dimensions of various subspaces of $M_{2}(3950, [\chi])$.

	Total	New	Old
Modular forms	57984	19200	38784
Cusp forms	57216	19200	38016
Eisenstein series	768	0	768

Trace form

19200 * q - 200 * q^4 - 4 * q^6 + 4 * q^7 - 200 * q^9 - 4 * q^10 + 16 * q^14 + 16 * q^15 - 200 * q^16 + 48 * q^17 + 32 * q^18 + 48 * q^21 + 44 * q^22 - 4 * q^23 - 192 * q^24 + 20 * q^25 - 198 * q^27 - 6 * q^28 - 24 * q^29 + 10 * q^30 - 84 * q^31 - 32 * q^33 - 8 * q^34 + 68 * q^35 - 200 * q^36 + 12 * q^37 + 8 * q^38 - 12 * q^39 + 2 * q^40 + 68 * q^41 + 10 * q^42 - 24 * q^43 - 50 * q^45 - 24 * q^47 + 804 * q^49 + 68 * q^50 + 36 * q^53 - 40 * q^54 - 24 * q^55 + 96 * q^56 - 128 * q^57 - 32 * q^58 - 168 * q^59 + 2 * q^60 + 72 * q^61 + 36 * q^62 + 80 * q^63 + 400 * q^64 - 112 * q^65 - 48 * q^66 - 128 * q^67 + 96 * q^68 + 116 * q^69 + 934 * q^70 - 72 * q^71 - 16 * q^72 - 56 * q^73 + 80 * q^74 - 98 * q^75 + 160 * q^77 - 240 * q^78 + 72 * q^79 - 176 * q^81 - 64 * q^82 + 414 * q^83 + 36 * q^84 - 236 * q^85 - 8 * q^86 - 362 * q^87 - 6 * q^88 + 48 * q^89 + 58 * q^90 + 116 * q^91 - 4 * q^92 - 112 * q^93 + 96 * q^94 + 388 * q^95 + 8 * q^96 + 64 * q^97 - 16 * q^98 + 20 * q^99

Decomposition of $S_{2}^{\mathrm{new}}(3950, [\chi])$ into newform subspaces

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

Decomposition of $S_{2}^{\mathrm{old}}(3950, [\chi])$ into lower level spaces

$S_{2}^{\mathrm{old}}(3950, [\chi]) \simeq$ $S_{2}^{\mathrm{new}}(1975, [\chi])$$^{\oplus 2}$