Properties

Label 74.5.i
Level $74$
Weight $5$
Character orbit 74.i
Rep. character $\chi_{74}(5,\cdot)$
Character field $\Q(\zeta_{36})$
Dimension $144$
Newform subspaces $2$
Sturm bound $47$
Trace bound $5$

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Defining parameters

Level: \( N \) \(=\) \( 74 = 2 \cdot 37 \)
Weight: \( k \) \(=\) \( 5 \)
Character orbit: \([\chi]\) \(=\) 74.i (of order \(36\) and degree \(12\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 37 \)
Character field: \(\Q(\zeta_{36})\)
Newform subspaces: \( 2 \)
Sturm bound: \(47\)
Trace bound: \(5\)
Distinguishing \(T_p\): \(3\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{5}(74, [\chi])\).

Total New Old
Modular forms 480 144 336
Cusp forms 432 144 288
Eisenstein series 48 0 48

Trace form

\( 144 q + 36 q^{5} - 420 q^{9} + O(q^{10}) \) \( 144 q + 36 q^{5} - 420 q^{9} - 480 q^{12} + 576 q^{14} + 1596 q^{15} - 720 q^{17} - 144 q^{19} + 288 q^{20} + 1476 q^{21} - 3996 q^{23} - 252 q^{25} - 1440 q^{26} - 11664 q^{27} - 3936 q^{28} + 1512 q^{29} + 6912 q^{30} + 19920 q^{31} + 8208 q^{33} + 4032 q^{34} + 6912 q^{35} + 3144 q^{37} - 3456 q^{38} - 9180 q^{39} - 7680 q^{40} - 12168 q^{41} - 11904 q^{42} - 12432 q^{43} - 35640 q^{45} + 3840 q^{46} + 3564 q^{47} + 6912 q^{48} + 35868 q^{49} + 14976 q^{50} + 3780 q^{53} + 12672 q^{54} - 10908 q^{55} + 5472 q^{57} - 16800 q^{58} - 22572 q^{59} + 39888 q^{61} - 19008 q^{62} + 9360 q^{63} + 31356 q^{65} - 30828 q^{67} + 3168 q^{68} + 7716 q^{69} + 18816 q^{70} + 37728 q^{71} + 12960 q^{74} - 63648 q^{75} - 1152 q^{76} - 26496 q^{77} - 35328 q^{78} - 27744 q^{79} + 2304 q^{80} + 6216 q^{81} - 14208 q^{82} + 41400 q^{83} - 25272 q^{85} - 8064 q^{86} + 3816 q^{87} + 15360 q^{88} - 47448 q^{89} + 38880 q^{90} + 95460 q^{91} - 60480 q^{92} - 145992 q^{93} - 4608 q^{94} - 45612 q^{95} - 12588 q^{97} + 59904 q^{98} - 12372 q^{99} + O(q^{100}) \)

Decomposition of \(S_{5}^{\mathrm{new}}(74, [\chi])\) into newform subspaces

Label Dim. \(A\) Field CM Traces $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
74.5.i.a $72$ $7.649$ None \(0\) \(0\) \(-78\) \(0\)
74.5.i.b $72$ $7.649$ None \(0\) \(0\) \(114\) \(0\)

Decomposition of \(S_{5}^{\mathrm{old}}(74, [\chi])\) into lower level spaces

\( S_{5}^{\mathrm{old}}(74, [\chi]) \cong \) \(S_{5}^{\mathrm{new}}(37, [\chi])\)\(^{\oplus 2}\)