Properties

Label 1445.4.bb
Level $1445$
Weight $4$
Character orbit 1445.bb
Rep. character $\chi_{1445}(21,\cdot)$
Character field $\Q(\zeta_{68})$
Dimension $9792$
Sturm bound $612$

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Defining parameters

Level: \( N \) \(=\) \( 1445 = 5 \cdot 17^{2} \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 1445.bb (of order \(68\) and degree \(32\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 289 \)
Character field: \(\Q(\zeta_{68})\)
Sturm bound: \(612\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{4}(1445, [\chi])\).

Total New Old
Modular forms 14784 9792 4992
Cusp forms 14656 9792 4864
Eisenstein series 128 0 128

Trace form

\( 9792 q + 4 q^{3} + 2448 q^{4} + 28 q^{6} - 960 q^{10} - 148 q^{11} - 268 q^{12} - 72 q^{13} + 84 q^{14} - 9528 q^{16} + 72 q^{17} + 216 q^{18} + 40 q^{20} + 320 q^{22} + 72 q^{23} + 7028 q^{24} + 160 q^{27}+ \cdots - 4580 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Decomposition of \(S_{4}^{\mathrm{new}}(1445, [\chi])\) into newform subspaces

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

Decomposition of \(S_{4}^{\mathrm{old}}(1445, [\chi])\) into lower level spaces

\( S_{4}^{\mathrm{old}}(1445, [\chi]) \simeq \) \(S_{4}^{\mathrm{new}}(289, [\chi])\)\(^{\oplus 2}\)