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Properties

Label 342.5.c
Level $342$
Weight $5$
Character orbit 342.c
Rep. character $\chi_{342}(305,\cdot)$
Character field $\Q$
Dimension $24$
Newform subspaces $2$
Sturm bound $300$
Trace bound $10$

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Defining parameters

Level: \( N \) \(=\) \( 342 = 2 \cdot 3^{2} \cdot 19 \)
Weight: \( k \) \(=\) \( 5 \)
Character orbit: \([\chi]\) \(=\) 342.c (of order \(2\) and degree \(1\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 3 \)
Character field: \(\Q\)
Newform subspaces: \( 2 \)
Sturm bound: \(300\)
Trace bound: \(10\)
Distinguishing \(T_p\): \(5\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{5}(342, [\chi])\).

Total New Old
Modular forms 248 24 224
Cusp forms 232 24 208
Eisenstein series 16 0 16

Trace form

\( 24 q - 192 q^{4} - 160 q^{7} + O(q^{10}) \) \( 24 q - 192 q^{4} - 160 q^{7} + 160 q^{13} + 1536 q^{16} + 1280 q^{22} - 3288 q^{25} + 1280 q^{28} - 3920 q^{31} + 2048 q^{34} - 4480 q^{37} + 2200 q^{43} + 1280 q^{46} + 8256 q^{49} - 1280 q^{52} - 648 q^{55} - 768 q^{58} + 20448 q^{61} - 12288 q^{64} - 752 q^{67} - 3840 q^{70} - 18712 q^{73} - 8944 q^{79} - 21760 q^{82} + 39240 q^{85} - 10240 q^{88} - 2896 q^{91} - 23296 q^{94} + 43152 q^{97} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{5}^{\mathrm{new}}(342, [\chi])\) into newform subspaces

Label Char Prim Dim $A$ Field CM Minimal twist Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
342.5.c.a 342.c 3.b $12$ $35.353$ \(\mathbb{Q}[x]/(x^{12} + \cdots)\) None 342.5.c.a \(0\) \(0\) \(0\) \(-80\) $\mathrm{SU}(2)[C_{2}]$ \(q-2\beta _{6}q^{2}-8q^{4}+(-2\beta _{6}-\beta _{7})q^{5}+\cdots\)
342.5.c.b 342.c 3.b $12$ $35.353$ \(\mathbb{Q}[x]/(x^{12} - \cdots)\) None 342.5.c.b \(0\) \(0\) \(0\) \(-80\) $\mathrm{SU}(2)[C_{2}]$ \(q+2\beta _{2}q^{2}-8q^{4}+(-\beta _{2}-\beta _{4})q^{5}+\cdots\)

Decomposition of \(S_{5}^{\mathrm{old}}(342, [\chi])\) into lower level spaces

\( S_{5}^{\mathrm{old}}(342, [\chi]) \simeq \) \(S_{5}^{\mathrm{new}}(6, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{5}^{\mathrm{new}}(9, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{5}^{\mathrm{new}}(18, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{5}^{\mathrm{new}}(57, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{5}^{\mathrm{new}}(114, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{5}^{\mathrm{new}}(171, [\chi])\)\(^{\oplus 2}\)