Space of modular forms of level 1305, weight 2, and Character 1305.n

• Label: 1305.2.n
• Level: $1305$
• Weight: $2$
• Character orbit: 1305.n
• Rep. character: $\chi_{1305}(233,\cdot)$
• Character field: $\Q(\zeta_{4})$
• Dimension: $112$
• Sturm bound: $360$

Defining parameters

Level:	\( N \)	\(=\)	\( 1305 = 3^{2} \cdot 5 \cdot 29 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1305.n (of order \(4\) and degree \(2\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 15 \)
Character field:			\(\Q(i)\)
Sturm bound:			\(360\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(1305, [\chi])\).

	Total	New	Old
Modular forms	376	112	264
Cusp forms	344	112	232
Eisenstein series	32	0	32

Trace form

\( 112 q + 32 q^{10} - 128 q^{16} - 32 q^{25} + 64 q^{31} - 32 q^{37} + 48 q^{40} + 48 q^{43} - 48 q^{52} - 64 q^{61} + 64 q^{67} - 64 q^{70} + 80 q^{73} - 96 q^{76} + 32 q^{85} + 32 q^{91}+O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(1305, [\chi])\) into newform subspaces

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

Decomposition of \(S_{2}^{\mathrm{old}}(1305, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(1305, [\chi]) \simeq \) \(S_{2}^{\mathrm{new}}(45, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(435, [\chi])\)\(^{\oplus 2}\)