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Properties

Label 1815.4.j
Level $1815$
Weight $4$
Character orbit 1815.j
Rep. character $\chi_{1815}(967,\cdot)$
Character field $\Q(\zeta_{4})$
Dimension $648$
Sturm bound $1056$

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Defining parameters

Level: \( N \) \(=\) \( 1815 = 3 \cdot 5 \cdot 11^{2} \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 1815.j (of order \(4\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 55 \)
Character field: \(\Q(i)\)
Sturm bound: \(1056\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{4}(1815, [\chi])\).

Total New Old
Modular forms 1632 648 984
Cusp forms 1536 648 888
Eisenstein series 96 0 96

Trace form

\( 648 q + 32 q^{5} + O(q^{10}) \) \( 648 q + 32 q^{5} + 48 q^{12} + 168 q^{15} - 10144 q^{16} - 760 q^{20} - 224 q^{23} - 592 q^{25} - 128 q^{26} - 432 q^{31} - 23328 q^{36} - 1104 q^{37} - 2072 q^{38} - 816 q^{42} - 2400 q^{47} + 384 q^{48} + 1248 q^{53} + 7232 q^{56} + 4360 q^{58} + 768 q^{60} - 544 q^{67} - 3408 q^{70} - 448 q^{71} + 1344 q^{75} + 144 q^{78} - 11440 q^{80} - 52488 q^{81} + 32 q^{82} - 17088 q^{86} + 2304 q^{91} - 9080 q^{92} - 2736 q^{93} + 4104 q^{97} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{4}^{\mathrm{new}}(1815, [\chi])\) into newform subspaces

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

Decomposition of \(S_{4}^{\mathrm{old}}(1815, [\chi])\) into lower level spaces

\( S_{4}^{\mathrm{old}}(1815, [\chi]) \cong \) \(S_{4}^{\mathrm{new}}(55, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(165, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(605, [\chi])\)\(^{\oplus 2}\)