Space of modular forms of level 325, weight 4, and Character 325.o

• Label: 325.4.o
• Level: $325$
• Weight: $4$
• Character orbit: 325.o
• Rep. character: $\chi_{325}(74,\cdot)$
• Character field: $\Q(\zeta_{6})$
• Dimension: $124$
• Sturm bound: $140$

Defining parameters

Level:	\( N \)	\(=\)	\( 325 = 5^{2} \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	325.o (of order \(6\) and degree \(2\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 65 \)
Character field:			\(\Q(\zeta_{6})\)
Sturm bound:			\(140\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{4}(325, [\chi])\).

	Total	New	Old
Modular forms	220	132	88
Cusp forms	196	124	72
Eisenstein series	24	8	16

Trace form

124 * q + 250 * q^4 + 30 * q^6 + 592 * q^9 - 14 * q^11 - 440 * q^14 - 994 * q^16 - 150 * q^19 - 172 * q^21 + 184 * q^24 + 388 * q^26 + 306 * q^29 + 280 * q^31 - 1632 * q^34 - 2496 * q^36 - 358 * q^39 + 198 * q^41 + 1976 * q^44 - 190 * q^46 + 2760 * q^49 + 868 * q^51 + 1150 * q^54 - 4114 * q^56 + 942 * q^59 - 1414 * q^61 - 6088 * q^64 + 3924 * q^66 - 162 * q^69 + 566 * q^71 + 2126 * q^74 + 3052 * q^76 - 1632 * q^79 - 7598 * q^81 + 6404 * q^84 + 13584 * q^86 - 1346 * q^89 + 10502 * q^91 + 4298 * q^94 - 4740 * q^96 + 13032 * q^99

Decomposition of \(S_{4}^{\mathrm{new}}(325, [\chi])\) into newform subspaces

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

Decomposition of \(S_{4}^{\mathrm{old}}(325, [\chi])\) into lower level spaces

\( S_{4}^{\mathrm{old}}(325, [\chi]) \simeq \) \(S_{4}^{\mathrm{new}}(65, [\chi])\)\(^{\oplus 2}\)