Properties

Label 144.5.m
Level $144$
Weight $5$
Character orbit 144.m
Rep. character $\chi_{144}(19,\cdot)$
Character field $\Q(\zeta_{4})$
Dimension $78$
Newform subspaces $3$
Sturm bound $120$
Trace bound $4$

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Defining parameters

Level: \( N \) \(=\) \( 144 = 2^{4} \cdot 3^{2} \)
Weight: \( k \) \(=\) \( 5 \)
Character orbit: \([\chi]\) \(=\) 144.m (of order \(4\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 16 \)
Character field: \(\Q(i)\)
Newform subspaces: \( 3 \)
Sturm bound: \(120\)
Trace bound: \(4\)
Distinguishing \(T_p\): \(5\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{5}(144, [\chi])\).

Total New Old
Modular forms 200 82 118
Cusp forms 184 78 106
Eisenstein series 16 4 12

Trace form

\( 78 q + 2 q^{2} - 8 q^{4} + 2 q^{5} - 4 q^{7} - 88 q^{8} + O(q^{10}) \) \( 78 q + 2 q^{2} - 8 q^{4} + 2 q^{5} - 4 q^{7} - 88 q^{8} - 300 q^{10} + 98 q^{11} - 2 q^{13} + 112 q^{14} + 536 q^{16} + 4 q^{17} + 702 q^{19} - 700 q^{20} + 428 q^{22} + 1156 q^{23} + 716 q^{26} - 64 q^{28} + 866 q^{29} + 152 q^{32} - 4036 q^{34} + 3844 q^{35} - 1826 q^{37} + 2312 q^{38} + 4960 q^{40} - 7266 q^{43} - 4204 q^{44} + 4 q^{46} + 22634 q^{49} + 5814 q^{50} - 10196 q^{52} - 478 q^{53} + 11772 q^{55} - 8504 q^{56} - 13184 q^{58} - 10270 q^{59} + 3774 q^{61} - 10380 q^{62} + 9712 q^{64} - 2012 q^{65} + 446 q^{67} - 752 q^{68} - 18616 q^{70} + 19972 q^{71} - 424 q^{74} - 17900 q^{76} + 100 q^{77} + 12848 q^{80} - 14384 q^{82} - 6718 q^{83} - 12452 q^{85} + 5996 q^{86} + 30280 q^{88} + 3836 q^{91} + 26296 q^{92} + 14904 q^{94} - 4 q^{97} - 40722 q^{98} + O(q^{100}) \)

Decomposition of \(S_{5}^{\mathrm{new}}(144, [\chi])\) into newform subspaces

Label Char Prim Dim $A$ Field CM Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
144.5.m.a 144.m 16.f $14$ $14.885$ \(\mathbb{Q}[x]/(x^{14} - \cdots)\) None \(2\) \(0\) \(2\) \(-4\) $\mathrm{SU}(2)[C_{4}]$ \(q-\beta _{4}q^{2}+(-1+2\beta _{3}-\beta _{11})q^{4}+(-\beta _{2}+\cdots)q^{5}+\cdots\)
144.5.m.b 144.m 16.f $32$ $14.885$ None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{4}]$
144.5.m.c 144.m 16.f $32$ $14.885$ None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{4}]$

Decomposition of \(S_{5}^{\mathrm{old}}(144, [\chi])\) into lower level spaces

\( S_{5}^{\mathrm{old}}(144, [\chi]) \cong \) \(S_{5}^{\mathrm{new}}(16, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{5}^{\mathrm{new}}(48, [\chi])\)\(^{\oplus 2}\)