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Properties

Label 45.5.c
Level $45$
Weight $5$
Character orbit 45.c
Rep. character $\chi_{45}(26,\cdot)$
Character field $\Q$
Dimension $4$
Newform subspaces $1$
Sturm bound $30$
Trace bound $0$

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Defining parameters

Level: \( N \) \(=\) \( 45 = 3^{2} \cdot 5 \)
Weight: \( k \) \(=\) \( 5 \)
Character orbit: \([\chi]\) \(=\) 45.c (of order \(2\) and degree \(1\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 3 \)
Character field: \(\Q\)
Newform subspaces: \( 1 \)
Sturm bound: \(30\)
Trace bound: \(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{5}(45, [\chi])\).

Total New Old
Modular forms 28 4 24
Cusp forms 20 4 16
Eisenstein series 8 0 8

Trace form

\( 4 q - 28 q^{4} - 48 q^{7} - 100 q^{10} + 808 q^{13} + 164 q^{16} - 1760 q^{19} - 272 q^{22} - 500 q^{25} + 5376 q^{28} - 1656 q^{31} - 5408 q^{34} + 344 q^{37} + 2700 q^{40} + 5776 q^{43} - 5736 q^{46}+ \cdots + 27416 q^{97}+O(q^{100}) \) Copy content Toggle raw display

Decomposition of \(S_{5}^{\mathrm{new}}(45, [\chi])\) into newform subspaces

Label Char Prim Dim $A$ Field CM Minimal twist Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
45.5.c.a 45.c 3.b $4$ $4.652$ \(\Q(\sqrt{-2}, \sqrt{-5})\) None 45.5.c.a \(0\) \(0\) \(0\) \(-48\) $\mathrm{SU}(2)[C_{2}]$ \(q+(\beta _{1}+\beta _{2})q^{2}+(-7-2\beta _{3})q^{4}+5\beta _{2}q^{5}+\cdots\)

Decomposition of \(S_{5}^{\mathrm{old}}(45, [\chi])\) into lower level spaces

\( S_{5}^{\mathrm{old}}(45, [\chi]) \simeq \) \(S_{5}^{\mathrm{new}}(9, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{5}^{\mathrm{new}}(15, [\chi])\)\(^{\oplus 2}\)