Properties

Label 45.3.c
Level $45$
Weight $3$
Character orbit 45.c
Rep. character $\chi_{45}(26,\cdot)$
Character field $\Q$
Dimension $4$
Newform subspaces $1$
Sturm bound $18$
Trace bound $0$

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Defining parameters

Level: \( N \) \(=\) \( 45 = 3^{2} \cdot 5 \)
Weight: \( k \) \(=\) \( 3 \)
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: \(18\)
Trace bound: \(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{3}(45, [\chi])\).

Total New Old
Modular forms 16 4 12
Cusp forms 8 4 4
Eisenstein series 8 0 8

Trace form

\( 4 q - 12 q^{4} + 16 q^{7} + O(q^{10}) \) \( 4 q - 12 q^{4} + 16 q^{7} - 20 q^{10} - 24 q^{13} + 84 q^{16} - 16 q^{22} - 20 q^{25} - 128 q^{28} - 56 q^{31} + 128 q^{34} + 152 q^{37} + 60 q^{40} - 48 q^{43} + 24 q^{46} - 92 q^{49} - 328 q^{52} + 40 q^{55} + 328 q^{58} - 168 q^{61} - 44 q^{64} + 208 q^{67} - 120 q^{70} + 216 q^{73} - 160 q^{76} - 56 q^{79} - 152 q^{82} + 160 q^{85} + 384 q^{88} + 104 q^{91} - 256 q^{94} - 232 q^{97} + O(q^{100}) \)

Decomposition of \(S_{3}^{\mathrm{new}}(45, [\chi])\) into newform subspaces

Label Char Prim Dim $A$ Field CM Minimal twist Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
45.3.c.a 45.c 3.b $4$ $1.226$ \(\Q(\sqrt{-2}, \sqrt{-5})\) None 45.3.c.a \(0\) \(0\) \(0\) \(16\) $\mathrm{SU}(2)[C_{2}]$ \(q+(-\beta _{1}-\beta _{2})q^{2}+(-3-2\beta _{3})q^{4}+\cdots\)

Decomposition of \(S_{3}^{\mathrm{old}}(45, [\chi])\) into lower level spaces

\( S_{3}^{\mathrm{old}}(45, [\chi]) \simeq \) \(S_{3}^{\mathrm{new}}(15, [\chi])\)\(^{\oplus 2}\)