Space of modular forms of level 315, weight 10, and Character 315.i

• Label: 315.10.i
• Level: $315$
• Weight: $10$
• Character orbit: 315.i
• Rep. character: $\chi_{315}(106,\cdot)$
• Character field: $\Q(\zeta_{3})$
• Dimension: $432$
• Sturm bound: $480$

Defining parameters

Level:	\( N \)	\(=\)	\( 315 = 3^{2} \cdot 5 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 10 \)
Character orbit:	\([\chi]\)	\(=\)	315.i (of order \(3\) and degree \(2\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 9 \)
Character field:			\(\Q(\zeta_{3})\)
Sturm bound:			\(480\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{10}(315, [\chi])\).

	Total	New	Old
Modular forms	872	432	440
Cusp forms	856	432	424
Eisenstein series	16	0	16

Trace form

432 * q + 64 * q^2 + 292 * q^3 - 55296 * q^4 - 10460 * q^6 - 61992 * q^8 - 84916 * q^9 + 116112 * q^11 - 853176 * q^12 + 132500 * q^15 - 14155776 * q^16 + 1453272 * q^17 - 1922828 * q^18 - 1575720 * q^19 + 19208 * q^21 + 2113344 * q^22 + 6716184 * q^23 + 3047824 * q^24 - 84375000 * q^25 + 30727568 * q^26 - 30526208 * q^27 + 2821696 * q^29 + 12580000 * q^30 + 20064256 * q^32 - 38240684 * q^33 - 7595532 * q^34 - 24010000 * q^35 - 49798964 * q^36 - 31684672 * q^38 + 135110676 * q^39 - 29092500 * q^40 + 40797828 * q^41 - 3141612 * q^43 - 483415872 * q^44 - 33820000 * q^45 - 20937096 * q^46 + 153226032 * q^47 + 251973736 * q^48 - 1245197016 * q^49 + 25000000 * q^50 + 191134864 * q^51 - 214046388 * q^52 - 416493680 * q^53 + 90468080 * q^54 + 1253265012 * q^57 + 427576644 * q^58 + 336492708 * q^59 + 135680000 * q^60 - 307001592 * q^62 - 79559536 * q^63 + 5972898096 * q^64 + 308690000 * q^65 + 1884657452 * q^66 + 457995924 * q^67 - 348774980 * q^68 - 906644040 * q^69 + 45623504 * q^71 - 3414216868 * q^72 + 1014053256 * q^73 + 516497596 * q^74 + 114062500 * q^75 + 771709788 * q^76 + 562448656 * q^77 + 3797143680 * q^78 - 204676524 * q^79 - 2140780000 * q^80 - 388973012 * q^81 + 1565026488 * q^82 + 3101651104 * q^83 - 1437344244 * q^84 + 255015000 * q^85 - 364899336 * q^86 + 5578186872 * q^87 + 1623048192 * q^88 + 307045120 * q^89 - 691520000 * q^90 - 859346712 * q^91 + 2021062616 * q^92 + 576622752 * q^93 - 3583917900 * q^94 + 2655690000 * q^95 - 4780095052 * q^96 - 295426116 * q^97 - 737894528 * q^98 + 944973280 * q^99

Decomposition of \(S_{10}^{\mathrm{new}}(315, [\chi])\) into newform subspaces

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

Decomposition of \(S_{10}^{\mathrm{old}}(315, [\chi])\) into lower level spaces

\( S_{10}^{\mathrm{old}}(315, [\chi]) \simeq \) \(S_{10}^{\mathrm{new}}(9, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{10}^{\mathrm{new}}(45, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{10}^{\mathrm{new}}(63, [\chi])\)\(^{\oplus 2}\)