Space of modular forms of level 1305, weight 4, and Character 1305.k

• Label: 1305.4.k
• Level: $1305$
• Weight: $4$
• Character orbit: 1305.k
• Rep. character: $\chi_{1305}(568,\cdot)$
• Character field: $\Q(\zeta_{4})$
• Dimension: $446$
• Sturm bound: $720$

Defining parameters

Level:	\( N \)	\(=\)	\( 1305 = 3^{2} \cdot 5 \cdot 29 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	1305.k (of order \(4\) and degree \(2\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 145 \)
Character field:			\(\Q(i)\)
Sturm bound:			\(720\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{4}(1305, [\chi])\).

	Total	New	Old
Modular forms	1096	454	642
Cusp forms	1064	446	618
Eisenstein series	32	8	24

Trace form

446 * q - 1768 * q^4 - 4 * q^7 + 18 * q^10 - 4 * q^11 - 234 * q^13 + 56 * q^14 + 6936 * q^16 + 260 * q^20 + 32 * q^22 + 4 * q^23 + 150 * q^25 - 216 * q^26 + 32 * q^28 + 124 * q^31 + 352 * q^34 - 496 * q^35 + 348 * q^37 + 844 * q^38 - 202 * q^40 - 606 * q^41 - 1044 * q^43 + 1128 * q^44 + 1244 * q^46 - 780 * q^47 + 1330 * q^50 + 2564 * q^52 - 662 * q^53 - 832 * q^55 - 628 * q^56 + 420 * q^58 + 862 * q^61 + 436 * q^62 - 29712 * q^64 - 1050 * q^65 - 96 * q^67 - 1908 * q^70 - 684 * q^76 - 4572 * q^80 + 3484 * q^82 - 3684 * q^83 + 656 * q^85 + 1324 * q^88 + 2450 * q^89 - 892 * q^92 + 5176 * q^95 + 9240 * q^97 + 5516 * q^98

Decomposition of \(S_{4}^{\mathrm{new}}(1305, [\chi])\) into newform subspaces

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

Decomposition of \(S_{4}^{\mathrm{old}}(1305, [\chi])\) into lower level spaces

\( S_{4}^{\mathrm{old}}(1305, [\chi]) \simeq \) \(S_{4}^{\mathrm{new}}(145, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(435, [\chi])\)\(^{\oplus 2}\)