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

• Label: 1275.4.bd
• Level: $1275$
• Weight: $4$
• Character orbit: 1275.bd
• Rep. character: $\chi_{1275}(16,\cdot)$
• Character field: $\Q(\zeta_{10})$
• Dimension: $1072$
• Sturm bound: $720$

Defining parameters

Level:	\( N \)	\(=\)	\( 1275 = 3 \cdot 5^{2} \cdot 17 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	1275.bd (of order \(10\) and degree \(4\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 425 \)
Character field:			\(\Q(\zeta_{10})\)
Sturm bound:			\(720\)

Dimensions

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

	Total	New	Old
Modular forms	2176	1072	1104
Cusp forms	2144	1072	1072
Eisenstein series	32	0	32

Trace form

1072 * q + 8 * q^2 - 1056 * q^4 + 96 * q^8 + 2412 * q^9 + 336 * q^13 - 12 * q^15 - 4096 * q^16 - 104 * q^17 + 288 * q^18 - 340 * q^19 + 168 * q^21 - 720 * q^25 + 144 * q^26 - 1536 * q^30 - 3584 * q^32 + 288 * q^33 - 372 * q^34 + 2088 * q^35 + 9504 * q^36 - 1720 * q^38 + 424 * q^43 + 976 * q^47 - 49200 * q^49 - 760 * q^50 + 3488 * q^52 + 576 * q^53 - 1796 * q^55 - 984 * q^59 - 192 * q^60 - 15360 * q^64 - 1056 * q^66 - 4256 * q^67 + 6912 * q^68 + 480 * q^69 - 3828 * q^70 - 864 * q^72 + 12544 * q^76 + 6192 * q^77 - 21708 * q^81 + 7160 * q^83 - 4752 * q^84 - 4596 * q^85 + 7320 * q^86 + 504 * q^87 - 4464 * q^89 - 10752 * q^93 - 12396 * q^94 - 4308 * 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

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