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Properties

Label 74.7.d
Level $74$
Weight $7$
Character orbit 74.d
Rep. character $\chi_{74}(31,\cdot)$
Character field $\Q(\zeta_{4})$
Dimension $38$
Newform subspaces $2$
Sturm bound $66$
Trace bound $1$

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Defining parameters

Level: \( N \) \(=\) \( 74 = 2 \cdot 37 \)
Weight: \( k \) \(=\) \( 7 \)
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: \(66\)
Trace bound: \(1\)
Distinguishing \(T_p\): \(3\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{7}(74, [\chi])\).

Total New Old
Modular forms 118 38 80
Cusp forms 110 38 72
Eisenstein series 8 0 8

Trace form

\( 38 q - 8 q^{2} + 354 q^{5} + 256 q^{8} - 10514 q^{9} + O(q^{10}) \) \( 38 q - 8 q^{2} + 354 q^{5} + 256 q^{8} - 10514 q^{9} + 1872 q^{10} - 4096 q^{12} - 5206 q^{13} - 832 q^{14} - 4272 q^{15} - 38912 q^{16} + 6866 q^{17} + 9720 q^{18} + 11416 q^{19} + 11328 q^{20} + 17856 q^{22} - 57056 q^{23} - 66608 q^{26} - 44914 q^{29} + 100304 q^{31} + 8192 q^{32} - 103680 q^{33} - 201072 q^{34} - 42304 q^{35} - 255860 q^{37} + 29920 q^{38} + 152584 q^{39} + 442496 q^{42} + 112 q^{43} - 949206 q^{45} - 352800 q^{46} + 64016 q^{47} + 1354810 q^{49} - 286152 q^{50} + 174040 q^{51} - 166592 q^{52} + 611576 q^{53} - 283680 q^{54} - 1235136 q^{55} + 26624 q^{56} + 1119512 q^{57} - 558080 q^{59} + 136704 q^{60} + 1345502 q^{61} + 128880 q^{63} + 326272 q^{66} + 219712 q^{68} - 1012216 q^{69} + 1332864 q^{70} - 297216 q^{71} - 311040 q^{72} - 1058024 q^{74} + 2496968 q^{75} + 365312 q^{76} - 772736 q^{79} - 362496 q^{80} + 5694230 q^{81} - 1962288 q^{82} + 3086920 q^{83} + 124416 q^{84} - 1048416 q^{86} - 3287824 q^{87} + 571392 q^{88} + 196278 q^{89} - 124080 q^{90} - 918720 q^{91} - 1825792 q^{92} + 2169984 q^{93} + 1601472 q^{94} - 1492138 q^{97} + 914248 q^{98} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{7}^{\mathrm{new}}(74, [\chi])\) into newform subspaces

Label Char Prim Dim $A$ Field CM Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
74.7.d.a 74.d 37.d $18$ $17.024$ \(\mathbb{Q}[x]/(x^{18} + \cdots)\) None \(72\) \(0\) \(294\) \(-104\) $\mathrm{SU}(2)[C_{4}]$ \(q+(4-4\beta _{6})q^{2}+(\beta _{1}-4\beta _{6})q^{3}-2^{5}\beta _{6}q^{4}+\cdots\)
74.7.d.b 74.d 37.d $20$ $17.024$ \(\mathbb{Q}[x]/(x^{20} + \cdots)\) None \(-80\) \(0\) \(60\) \(104\) $\mathrm{SU}(2)[C_{4}]$ \(q+(-4-4\beta _{6})q^{2}+(-\beta _{1}+3\beta _{6})q^{3}+\cdots\)

Decomposition of \(S_{7}^{\mathrm{old}}(74, [\chi])\) into lower level spaces

\( S_{7}^{\mathrm{old}}(74, [\chi]) \cong \) \(S_{7}^{\mathrm{new}}(37, [\chi])\)\(^{\oplus 2}\)