Space of modular forms of level 1275, weight 4, and Character 1275.bq

• Label: 1275.4.bq
• Level: $1275$
• Weight: $4$
• Character orbit: 1275.bq
• Rep. character: $\chi_{1275}(82,\cdot)$
• Character field: $\Q(\zeta_{16})$
• Dimension: $1296$
• Sturm bound: $720$

Defining parameters

Level:	\( N \)	\(=\)	\( 1275 = 3 \cdot 5^{2} \cdot 17 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	1275.bq (of order \(16\) and degree \(8\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 85 \)
Character field:			\(\Q(\zeta_{16})\)
Sturm bound:			\(720\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{4}(1275, [\chi])\).

	Total	New	Old
Modular forms	4416	1296	3120
Cusp forms	4224	1296	2928
Eisenstein series	192	0	192

Trace form

1296 * q + 1664 * q^14 - 192 * q^19 + 2944 * q^26 + 512 * q^28 - 1728 * q^31 - 768 * q^33 + 1152 * q^34 - 864 * q^36 + 864 * q^37 - 1840 * q^41 + 3936 * q^46 - 3072 * q^52 + 6096 * q^53 - 864 * q^54 - 1536 * q^57 + 2576 * q^58 - 3968 * q^59 + 8448 * q^64 + 192 * q^67 - 22544 * q^68 - 6272 * q^71 - 3456 * q^72 - 1440 * q^73 + 9760 * q^74 + 1536 * q^76 - 9888 * q^77 + 2688 * q^78 + 8192 * q^79 + 2560 * q^82 + 15008 * q^83 - 576 * q^84 + 10496 * q^86 + 3744 * q^87 + 5680 * q^88 + 11360 * q^92 + 5856 * q^93 - 8544 * q^94 - 6144 * q^96 - 4608 * q^97 - 14112 * q^98

Decomposition of \(S_{4}^{\mathrm{new}}(1275, [\chi])\) into newform subspaces

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

Decomposition of \(S_{4}^{\mathrm{old}}(1275, [\chi])\) into lower level spaces

\( S_{4}^{\mathrm{old}}(1275, [\chi]) \simeq \) \(S_{4}^{\mathrm{new}}(85, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(255, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(425, [\chi])\)\(^{\oplus 2}\)