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Properties

Label 342.5.d
Level $342$
Weight $5$
Character orbit 342.d
Rep. character $\chi_{342}(37,\cdot)$
Character field $\Q$
Dimension $32$
Newform subspaces $3$
Sturm bound $300$
Trace bound $5$

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Defining parameters

Level: \( N \) \(=\) \( 342 = 2 \cdot 3^{2} \cdot 19 \)
Weight: \( k \) \(=\) \( 5 \)
Character orbit: \([\chi]\) \(=\) 342.d (of order \(2\) and degree \(1\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 19 \)
Character field: \(\Q\)
Newform subspaces: \( 3 \)
Sturm bound: \(300\)
Trace bound: \(5\)
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 32 216
Cusp forms 232 32 200
Eisenstein series 16 0 16

Trace form

\( 32 q - 256 q^{4} + 18 q^{5} - 2 q^{7} + O(q^{10}) \) \( 32 q - 256 q^{4} + 18 q^{5} - 2 q^{7} - 342 q^{11} + 2048 q^{16} - 1242 q^{17} + 1028 q^{19} - 144 q^{20} - 1356 q^{23} + 2394 q^{25} - 192 q^{26} + 16 q^{28} - 1374 q^{35} + 1296 q^{38} + 5866 q^{43} + 2736 q^{44} + 6426 q^{47} + 2934 q^{49} + 3986 q^{55} - 1728 q^{58} + 5122 q^{61} - 2496 q^{62} - 16384 q^{64} + 9936 q^{68} + 286 q^{73} - 7776 q^{74} - 8224 q^{76} + 5658 q^{77} + 1152 q^{80} + 4992 q^{82} + 29712 q^{83} - 4174 q^{85} + 10848 q^{92} + 18882 q^{95} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

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

Label Char Prim Dim $A$ Field CM Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
342.5.d.a 342.d 19.b $8$ $35.353$ \(\mathbb{Q}[x]/(x^{8} + \cdots)\) None \(0\) \(0\) \(-18\) \(-162\) $\mathrm{SU}(2)[C_{2}]$ \(q+\beta _{2}q^{2}-8q^{4}+(-2+\beta _{6})q^{5}+(-20+\cdots)q^{7}+\cdots\)
342.5.d.b 342.d 19.b $12$ $35.353$ \(\mathbb{Q}[x]/(x^{12} + \cdots)\) None \(0\) \(0\) \(0\) \(20\) $\mathrm{SU}(2)[C_{2}]$ \(q-\beta _{7}q^{2}-8q^{4}-\beta _{1}q^{5}+(2-\beta _{2})q^{7}+\cdots\)
342.5.d.c 342.d 19.b $12$ $35.353$ \(\mathbb{Q}[x]/(x^{12} - \cdots)\) None \(0\) \(0\) \(36\) \(140\) $\mathrm{SU}(2)[C_{2}]$ \(q+\beta _{5}q^{2}-8q^{4}+(3-\beta _{7})q^{5}+(12-\beta _{2}+\cdots)q^{7}+\cdots\)

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

\( S_{5}^{\mathrm{old}}(342, [\chi]) \cong \) \(S_{5}^{\mathrm{new}}(19, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{5}^{\mathrm{new}}(38, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{5}^{\mathrm{new}}(57, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{5}^{\mathrm{new}}(114, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{5}^{\mathrm{new}}(171, [\chi])\)\(^{\oplus 2}\)