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Properties

Label 414.3.k
Level $414$
Weight $3$
Character orbit 414.k
Rep. character $\chi_{414}(35,\cdot)$
Character field $\Q(\zeta_{22})$
Dimension $160$
Newform subspaces $2$
Sturm bound $216$
Trace bound $7$

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Defining parameters

Level: \( N \) \(=\) \( 414 = 2 \cdot 3^{2} \cdot 23 \)
Weight: \( k \) \(=\) \( 3 \)
Character orbit: \([\chi]\) \(=\) 414.k (of order \(22\) and degree \(10\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 69 \)
Character field: \(\Q(\zeta_{22})\)
Newform subspaces: \( 2 \)
Sturm bound: \(216\)
Trace bound: \(7\)
Distinguishing \(T_p\): \(5\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{3}(414, [\chi])\).

Total New Old
Modular forms 1520 160 1360
Cusp forms 1360 160 1200
Eisenstein series 160 0 160

Trace form

\( 160 q + 32 q^{4} + O(q^{10}) \) \( 160 q + 32 q^{4} - 16 q^{13} - 64 q^{16} + 80 q^{19} + 32 q^{22} - 96 q^{25} + 32 q^{31} - 32 q^{34} - 640 q^{37} + 16 q^{43} - 48 q^{46} + 64 q^{49} + 32 q^{52} + 1640 q^{55} + 880 q^{58} + 944 q^{61} + 128 q^{64} + 104 q^{67} - 224 q^{70} - 152 q^{73} - 160 q^{76} - 1312 q^{79} - 912 q^{82} - 1800 q^{85} - 64 q^{88} - 240 q^{91} - 480 q^{94} - 432 q^{97} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{3}^{\mathrm{new}}(414, [\chi])\) into newform subspaces

Label Char Prim Dim $A$ Field CM Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
414.3.k.a 414.k 69.h $80$ $11.281$ None \(0\) \(0\) \(0\) \(-16\) $\mathrm{SU}(2)[C_{22}]$
414.3.k.b 414.k 69.h $80$ $11.281$ None \(0\) \(0\) \(0\) \(16\) $\mathrm{SU}(2)[C_{22}]$

Decomposition of \(S_{3}^{\mathrm{old}}(414, [\chi])\) into lower level spaces

\( S_{3}^{\mathrm{old}}(414, [\chi]) \cong \) \(S_{3}^{\mathrm{new}}(69, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(138, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(207, [\chi])\)\(^{\oplus 2}\)