Properties

Label 74.5.d
Level $74$
Weight $5$
Character orbit 74.d
Rep. character $\chi_{74}(31,\cdot)$
Character field $\Q(\zeta_{4})$
Dimension $28$
Newform subspaces $2$
Sturm bound $47$
Trace bound $2$

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Defining parameters

Level: \( N \) \(=\) \( 74 = 2 \cdot 37 \)
Weight: \( k \) \(=\) \( 5 \)
Character orbit: \([\chi]\) \(=\) 74.d (of order \(4\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 37 \)
Character field: \(\Q(i)\)
Newform subspaces: \( 2 \)
Sturm bound: \(47\)
Trace bound: \(2\)
Distinguishing \(T_p\): \(3\)

Dimensions

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

Total New Old
Modular forms 80 28 52
Cusp forms 72 28 44
Eisenstein series 8 0 8

Trace form

\( 28 q + 24 q^{5} - 692 q^{9} + O(q^{10}) \) \( 28 q + 24 q^{5} - 692 q^{9} + 192 q^{10} + 320 q^{12} - 160 q^{13} - 192 q^{14} - 756 q^{15} - 1792 q^{16} + 168 q^{17} - 512 q^{19} + 192 q^{20} - 640 q^{22} - 348 q^{23} - 192 q^{26} + 1212 q^{29} + 3204 q^{31} + 2736 q^{33} + 3456 q^{34} + 324 q^{35} + 96 q^{37} - 576 q^{38} - 5324 q^{39} - 6208 q^{42} + 5552 q^{43} + 3924 q^{45} + 2624 q^{46} - 1176 q^{47} + 20716 q^{49} + 6144 q^{50} - 9164 q^{51} - 1280 q^{52} - 7656 q^{53} - 1728 q^{54} + 19516 q^{55} + 1536 q^{56} - 8572 q^{57} - 12924 q^{59} + 6048 q^{60} - 18292 q^{61} + 19656 q^{63} + 2944 q^{66} + 1344 q^{68} + 23168 q^{69} - 13312 q^{70} - 2544 q^{71} + 6240 q^{74} - 56632 q^{75} - 4096 q^{76} - 8032 q^{79} - 1536 q^{80} - 35668 q^{81} + 18944 q^{82} - 42912 q^{83} - 23040 q^{84} + 6720 q^{86} + 21464 q^{87} - 5120 q^{88} + 32208 q^{89} - 33600 q^{90} - 10988 q^{91} - 2784 q^{92} - 13776 q^{93} - 25216 q^{94} + 39868 q^{97} + 9984 q^{98} + O(q^{100}) \)

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.d.a \(14\) \(7.649\) \(\mathbb{Q}[x]/(x^{14} + \cdots)\) None \(-28\) \(0\) \(-12\) \(48\) \(q+(-2+2\beta _{5})q^{2}+(\beta _{1}+\beta _{5})q^{3}-8\beta _{5}q^{4}+\cdots\)
74.5.d.b \(14\) \(7.649\) \(\mathbb{Q}[x]/(x^{14} + \cdots)\) None \(28\) \(0\) \(36\) \(-48\) \(q+(2+2\beta _{5})q^{2}+(\beta _{1}-\beta _{5})q^{3}+8\beta _{5}q^{4}+\cdots\)

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

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