↑

Properties

Label 74.3.g
Level $74$
Weight $3$
Character orbit 74.g
Rep. character $\chi_{74}(23,\cdot)$
Character field $\Q(\zeta_{12})$
Dimension $20$
Newform subspaces $2$
Sturm bound $28$
Trace bound $1$

Related objects

Downloads

Learn more

Defining parameters

Level: \( N \) \(=\) \( 74 = 2 \cdot 37 \)
Weight: \( k \) \(=\) \( 3 \)
Character orbit: \([\chi]\) \(=\) 74.g (of order \(12\) and degree \(4\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 37 \)
Character field: \(\Q(\zeta_{12})\)
Newform subspaces: \( 2 \)
Sturm bound: \(28\)
Trace bound: \(1\)
Distinguishing \(T_p\): \(3\)

Dimensions

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

Total New Old
Modular forms 84 20 64
Cusp forms 68 20 48
Eisenstein series 16 0 16

Trace form

\( 20 q - 2 q^{2} + 12 q^{5} - 8 q^{8} + 26 q^{9} + O(q^{10}) \) \( 20 q - 2 q^{2} + 12 q^{5} - 8 q^{8} + 26 q^{9} - 12 q^{10} - 8 q^{12} + 6 q^{13} + 32 q^{14} - 72 q^{15} + 40 q^{16} + 14 q^{17} + 30 q^{18} - 96 q^{19} + 24 q^{20} + 36 q^{21} - 16 q^{22} - 56 q^{23} - 18 q^{25} - 104 q^{26} - 24 q^{28} - 22 q^{29} - 144 q^{30} + 40 q^{31} + 8 q^{32} - 24 q^{33} - 18 q^{34} - 16 q^{35} - 136 q^{37} + 16 q^{38} + 188 q^{39} + 60 q^{40} + 204 q^{41} - 80 q^{42} + 232 q^{43} + 78 q^{45} + 104 q^{46} - 64 q^{47} + 6 q^{49} + 216 q^{50} - 244 q^{51} + 12 q^{52} - 28 q^{53} + 216 q^{54} - 32 q^{55} + 32 q^{56} + 316 q^{57} + 210 q^{58} - 320 q^{59} - 24 q^{60} + 522 q^{61} - 216 q^{62} - 792 q^{63} - 102 q^{65} + 32 q^{66} + 60 q^{67} + 4 q^{68} - 68 q^{69} + 80 q^{70} + 144 q^{71} - 60 q^{72} + 4 q^{74} - 200 q^{75} - 192 q^{76} + 96 q^{77} - 384 q^{78} + 160 q^{79} + 120 q^{80} + 286 q^{81} + 20 q^{82} - 56 q^{83} - 96 q^{84} - 72 q^{86} + 616 q^{87} + 64 q^{88} - 78 q^{89} - 90 q^{90} + 748 q^{91} - 112 q^{92} - 876 q^{93} - 16 q^{94} - 348 q^{95} - 214 q^{97} - 302 q^{98} - 408 q^{99} + O(q^{100}) \)

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.g.a 74.g 37.g $8$ $2.016$ 8.0.303595776.1 None \(4\) \(0\) \(12\) \(8\) $\mathrm{SU}(2)[C_{12}]$ \(q+(-\beta _{4}+\beta _{5})q^{2}+(2\beta _{1}-\beta _{5}-\beta _{7})q^{3}+\cdots\)
74.3.g.b 74.g 37.g $12$ $2.016$ \(\mathbb{Q}[x]/(x^{12} + \cdots)\) None \(-6\) \(0\) \(0\) \(-8\) $\mathrm{SU}(2)[C_{12}]$ \(q+(\beta _{4}-\beta _{7})q^{2}-\beta _{3}q^{3}+2\beta _{6}q^{4}+(1+\cdots)q^{5}+\cdots\)

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

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