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Properties

Label 348.2.c
Level $348$
Weight $2$
Character orbit 348.c
Rep. character $\chi_{348}(59,\cdot)$
Character field $\Q$
Dimension $56$
Newform subspaces $2$
Sturm bound $120$
Trace bound $1$

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Defining parameters

Level: \( N \) \(=\) \( 348 = 2^{2} \cdot 3 \cdot 29 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 348.c (of order \(2\) and degree \(1\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 12 \)
Character field: \(\Q\)
Newform subspaces: \( 2 \)
Sturm bound: \(120\)
Trace bound: \(1\)
Distinguishing \(T_p\): \(5\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(348, [\chi])\).

Total New Old
Modular forms 64 56 8
Cusp forms 56 56 0
Eisenstein series 8 0 8

Trace form

\( 56 q - 4 q^{4} - 4 q^{9} + O(q^{10}) \) \( 56 q - 4 q^{4} - 4 q^{9} + 4 q^{10} + 10 q^{12} - 8 q^{13} + 12 q^{16} + 10 q^{18} - 2 q^{22} + 6 q^{24} - 56 q^{25} + 6 q^{28} - 4 q^{30} - 16 q^{33} + 26 q^{34} - 16 q^{36} + 8 q^{37} + 30 q^{42} + 24 q^{45} - 44 q^{46} + 6 q^{48} - 32 q^{49} + 6 q^{52} - 28 q^{54} + 8 q^{57} - 34 q^{60} - 24 q^{61} - 34 q^{64} - 34 q^{66} - 8 q^{69} + 68 q^{70} + 22 q^{72} + 24 q^{76} - 30 q^{78} + 36 q^{81} - 12 q^{82} - 48 q^{84} + 16 q^{85} - 32 q^{88} - 26 q^{90} - 40 q^{93} - 66 q^{94} - 48 q^{97} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{2}^{\mathrm{new}}(348, [\chi])\) into newform subspaces

Label Char Prim Dim $A$ Field CM Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
348.2.c.a 348.c 12.b $16$ $2.779$ \(\mathbb{Q}[x]/(x^{16} - \cdots)\) None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+\beta _{4}q^{2}+\beta _{1}q^{3}+(\beta _{2}+\beta _{9}+\beta _{11}+\cdots)q^{4}+\cdots\)
348.2.c.b 348.c 12.b $40$ $2.779$ None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$