Space of modular forms of level 315, weight 4, and Character 315.i

• Label: 315.4.i
• Level: $315$
• Weight: $4$
• Character orbit: 315.i
• Rep. character: $\chi_{315}(106,\cdot)$
• Character field: $\Q(\zeta_{3})$
• Dimension: $144$
• Sturm bound: $192$

Defining parameters

Level:	\( N \)	\(=\)	\( 315 = 3^{2} \cdot 5 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	315.i (of order \(3\) and degree \(2\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 9 \)
Character field:			\(\Q(\zeta_{3})\)
Sturm bound:			\(192\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{4}(315, [\chi])\).

	Total	New	Old
Modular forms	296	144	152
Cusp forms	280	144	136
Eisenstein series	16	0	16

Trace form

144 * q - 8 * q^2 + 4 * q^3 - 288 * q^4 - 20 * q^6 + 216 * q^8 - 28 * q^9 - 96 * q^11 - 408 * q^12 + 20 * q^15 - 1152 * q^16 + 456 * q^17 + 4 * q^18 - 360 * q^19 + 56 * q^21 + 72 * q^22 - 552 * q^23 + 1072 * q^24 - 1800 * q^25 - 3184 * q^26 - 224 * q^27 + 448 * q^29 + 160 * q^30 - 992 * q^32 + 2332 * q^33 - 756 * q^34 + 560 * q^35 + 412 * q^36 - 424 * q^38 + 948 * q^39 - 180 * q^40 + 396 * q^41 - 684 * q^43 - 96 * q^44 - 160 * q^45 - 72 * q^46 + 816 * q^47 - 1208 * q^48 - 3528 * q^49 - 200 * q^50 + 928 * q^51 + 1836 * q^52 + 1840 * q^53 - 280 * q^54 + 1116 * q^57 + 1188 * q^58 - 1596 * q^59 + 320 * q^60 + 2664 * q^62 - 112 * q^63 + 6768 * q^64 - 1360 * q^65 - 6916 * q^66 - 1548 * q^67 + 940 * q^68 - 600 * q^69 + 848 * q^71 + 6716 * q^72 - 4968 * q^73 + 2428 * q^74 + 100 * q^75 + 3276 * q^76 - 1232 * q^77 + 6960 * q^78 + 468 * q^79 + 4640 * q^80 + 5476 * q^81 + 6984 * q^82 + 1408 * q^83 - 2772 * q^84 + 360 * q^85 + 48 * q^86 - 10824 * q^87 + 864 * q^88 - 11840 * q^89 - 320 * q^90 - 504 * q^91 - 5032 * q^92 - 3936 * q^93 - 2700 * q^94 - 4080 * q^95 - 3244 * q^96 - 108 * q^97 + 784 * q^98 - 8000 * q^99

Decomposition of \(S_{4}^{\mathrm{new}}(315, [\chi])\) into newform subspaces

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

Decomposition of \(S_{4}^{\mathrm{old}}(315, [\chi])\) into lower level spaces

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