Properties

Label 405.3.c
Level $405$
Weight $3$
Character orbit 405.c
Rep. character $\chi_{405}(161,\cdot)$
Character field $\Q$
Dimension $32$
Newform subspaces $2$
Sturm bound $162$
Trace bound $7$

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Defining parameters

Level: \( N \) \(=\) \( 405 = 3^{4} \cdot 5 \)
Weight: \( k \) \(=\) \( 3 \)
Character orbit: \([\chi]\) \(=\) 405.c (of order \(2\) and degree \(1\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 3 \)
Character field: \(\Q\)
Newform subspaces: \( 2 \)
Sturm bound: \(162\)
Trace bound: \(7\)
Distinguishing \(T_p\): \(2\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{3}(405, [\chi])\).

Total New Old
Modular forms 120 32 88
Cusp forms 96 32 64
Eisenstein series 24 0 24

Trace form

\( 32 q - 64 q^{4} + 4 q^{7} + O(q^{10}) \) \( 32 q - 64 q^{4} + 4 q^{7} - 20 q^{13} + 104 q^{16} + 4 q^{19} + 168 q^{22} - 160 q^{25} - 200 q^{28} + 64 q^{31} - 84 q^{34} - 44 q^{37} - 60 q^{40} - 8 q^{43} + 324 q^{46} + 324 q^{49} + 196 q^{52} - 492 q^{58} - 116 q^{61} - 40 q^{64} - 260 q^{67} + 120 q^{70} - 212 q^{73} + 76 q^{76} + 328 q^{79} - 204 q^{82} - 60 q^{85} - 360 q^{88} + 608 q^{91} + 204 q^{94} + 412 q^{97} + O(q^{100}) \)

Decomposition of \(S_{3}^{\mathrm{new}}(405, [\chi])\) into newform subspaces

Label Char Prim Dim $A$ Field CM Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
405.3.c.a 405.c 3.b $16$ $11.035$ \(\mathbb{Q}[x]/(x^{16} + \cdots)\) None \(0\) \(0\) \(0\) \(-4\) $\mathrm{SU}(2)[C_{2}]$ \(q+\beta _{1}q^{2}+(-2+\beta _{2})q^{4}+\beta _{10}q^{5}+\cdots\)
405.3.c.b 405.c 3.b $16$ $11.035$ \(\mathbb{Q}[x]/(x^{16} + \cdots)\) None \(0\) \(0\) \(0\) \(8\) $\mathrm{SU}(2)[C_{2}]$ \(q-\beta _{3}q^{2}+(-2-\beta _{11})q^{4}+\beta _{2}q^{5}+\cdots\)

Decomposition of \(S_{3}^{\mathrm{old}}(405, [\chi])\) into lower level spaces

\( S_{3}^{\mathrm{old}}(405, [\chi]) \cong \) \(S_{3}^{\mathrm{new}}(15, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(27, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(45, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(81, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(135, [\chi])\)\(^{\oplus 2}\)