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Properties

Label 74.3.d
Level $74$
Weight $3$
Character orbit 74.d
Rep. character $\chi_{74}(31,\cdot)$
Character field $\Q(\zeta_{4})$
Dimension $10$
Newform subspaces $4$
Sturm bound $28$
Trace bound $6$

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Defining parameters

Level: \( N \) \(=\) \( 74 = 2 \cdot 37 \)
Weight: \( k \) \(=\) \( 3 \)
Character orbit: \([\chi]\) \(=\) 74.d (of order \(4\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 37 \)
Character field: \(\Q(i)\)
Newform subspaces: \( 4 \)
Sturm bound: \(28\)
Trace bound: \(6\)
Distinguishing \(T_p\): \(3\), \(5\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{3}(74, [\chi])\).

Total New Old
Modular forms 42 10 32
Cusp forms 34 10 24
Eisenstein series 8 0 8

Trace form

\( 10 q + 2 q^{2} - 6 q^{5} - 4 q^{8} + 34 q^{9} + O(q^{10}) \) \( 10 q + 2 q^{2} - 6 q^{5} - 4 q^{8} + 34 q^{9} + 12 q^{10} - 16 q^{12} - 6 q^{13} + 16 q^{14} - 12 q^{15} - 40 q^{16} + 10 q^{17} - 30 q^{18} + 24 q^{19} - 12 q^{20} + 16 q^{22} - 52 q^{23} + 44 q^{26} - 62 q^{29} - 100 q^{31} - 8 q^{32} - 48 q^{33} - 36 q^{34} + 76 q^{35} + 28 q^{37} + 8 q^{38} + 100 q^{39} + 32 q^{42} - 64 q^{43} - 186 q^{45} + 136 q^{46} + 328 q^{47} - 114 q^{49} + 18 q^{50} + 244 q^{51} - 12 q^{52} + 64 q^{53} + 72 q^{54} - 76 q^{55} - 32 q^{56} + 116 q^{57} - 244 q^{59} + 24 q^{60} - 126 q^{61} + 72 q^{63} - 32 q^{66} + 20 q^{68} - 88 q^{69} - 416 q^{70} + 48 q^{71} + 60 q^{72} + 266 q^{74} + 128 q^{75} + 48 q^{76} + 32 q^{79} + 24 q^{80} - 22 q^{81} - 116 q^{82} - 184 q^{83} + 96 q^{84} + 24 q^{86} + 248 q^{87} + 32 q^{88} - 474 q^{89} - 180 q^{90} + 188 q^{91} - 104 q^{92} - 48 q^{93} + 16 q^{94} - 134 q^{97} - 274 q^{98} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{3}^{\mathrm{new}}(74, [\chi])\) into newform subspaces

Label Char Prim Dim $A$ Field CM Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
74.3.d.a 74.d 37.d $2$ $2.016$ \(\Q(\sqrt{-1}) \) None \(2\) \(0\) \(-12\) \(10\) $\mathrm{SU}(2)[C_{4}]$ \(q+(1+i)q^{2}+iq^{3}+2iq^{4}+(-6+6i)q^{5}+\cdots\)
74.3.d.b 74.d 37.d $2$ $2.016$ \(\Q(\sqrt{-1}) \) None \(2\) \(0\) \(6\) \(-8\) $\mathrm{SU}(2)[C_{4}]$ \(q+(1+i)q^{2}+4iq^{3}+2iq^{4}+(3-3i)q^{5}+\cdots\)
74.3.d.c 74.d 37.d $2$ $2.016$ \(\Q(\sqrt{-1}) \) None \(2\) \(0\) \(6\) \(6\) $\mathrm{SU}(2)[C_{4}]$ \(q+(1+i)q^{2}-3iq^{3}+2iq^{4}+(3-3i)q^{5}+\cdots\)
74.3.d.d 74.d 37.d $4$ $2.016$ \(\Q(i, \sqrt{65})\) None \(-4\) \(0\) \(-6\) \(-8\) $\mathrm{SU}(2)[C_{4}]$ \(q+(-1+\beta _{1})q^{2}-\beta _{1}q^{3}-2\beta _{1}q^{4}+\cdots\)

Decomposition of \(S_{3}^{\mathrm{old}}(74, [\chi])\) into lower level spaces

\( S_{3}^{\mathrm{old}}(74, [\chi]) \cong \) \(S_{3}^{\mathrm{new}}(37, [\chi])\)\(^{\oplus 2}\)