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Properties

Label 448.2.bc
Level $448$
Weight $2$
Character orbit 448.bc
Rep. character $\chi_{448}(29,\cdot)$
Character field $\Q(\zeta_{16})$
Dimension $384$
Newform subspaces $3$
Sturm bound $128$
Trace bound $1$

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Defining parameters

Level: \( N \) \(=\) \( 448 = 2^{6} \cdot 7 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 448.bc (of order \(16\) and degree \(8\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 64 \)
Character field: \(\Q(\zeta_{16})\)
Newform subspaces: \( 3 \)
Sturm bound: \(128\)
Trace bound: \(1\)
Distinguishing \(T_p\): \(3\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(448, [\chi])\).

Total New Old
Modular forms 528 384 144
Cusp forms 496 384 112
Eisenstein series 32 0 32

Trace form

\( 384 q + O(q^{10}) \) \( 384 q - 8 q^{22} - 80 q^{26} - 80 q^{30} - 80 q^{32} - 80 q^{34} - 80 q^{36} - 80 q^{40} - 8 q^{44} - 64 q^{51} + 128 q^{54} - 128 q^{55} + 56 q^{56} + 144 q^{58} + 96 q^{60} + 96 q^{62} - 80 q^{63} - 80 q^{67} + 96 q^{68} + 96 q^{70} + 144 q^{72} + 56 q^{74} - 128 q^{75} + 128 q^{76} - 48 q^{78} - 64 q^{79} - 128 q^{80} - 208 q^{86} - 160 q^{88} - 304 q^{92} - 192 q^{94} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{2}^{\mathrm{new}}(448, [\chi])\) into newform subspaces

Label Char Prim Dim $A$ Field CM Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
448.2.bc.a 448.bc 64.i $8$ $3.577$ \(\Q(\zeta_{16})\) None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{16}]$ \(q+(\zeta_{16}^{3}-\zeta_{16}^{7})q^{2}+(-\zeta_{16}-\zeta_{16}^{2}+\cdots)q^{3}+\cdots\)
448.2.bc.b 448.bc 64.i $184$ $3.577$ None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{16}]$
448.2.bc.c 448.bc 64.i $192$ $3.577$ None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{16}]$

Decomposition of \(S_{2}^{\mathrm{old}}(448, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(448, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(64, [\chi])\)\(^{\oplus 2}\)