Properties

Label 74.4.a
Level $74$
Weight $4$
Character orbit 74.a
Rep. character $\chi_{74}(1,\cdot)$
Character field $\Q$
Dimension $9$
Newform subspaces $4$
Sturm bound $38$
Trace bound $2$

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Defining parameters

Level: \( N \) \(=\) \( 74 = 2 \cdot 37 \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 74.a (trivial)
Character field: \(\Q\)
Newform subspaces: \( 4 \)
Sturm bound: \(38\)
Trace bound: \(2\)
Distinguishing \(T_p\): \(3\), \(5\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{4}(\Gamma_0(74))\).

Total New Old
Modular forms 31 9 22
Cusp forms 27 9 18
Eisenstein series 4 0 4

The following table gives the dimensions of the cuspidal new subspaces with specified eigenvalues for the Atkin-Lehner operators and the Fricke involution.

\(2\)\(37\)FrickeDim.
\(+\)\(+\)\(+\)\(3\)
\(+\)\(-\)\(-\)\(1\)
\(-\)\(+\)\(-\)\(1\)
\(-\)\(-\)\(+\)\(4\)
Plus space\(+\)\(7\)
Minus space\(-\)\(2\)

Trace form

\( 9 q + 2 q^{2} - 2 q^{3} + 36 q^{4} + 26 q^{5} + 4 q^{7} + 8 q^{8} + 127 q^{9} + O(q^{10}) \) \( 9 q + 2 q^{2} - 2 q^{3} + 36 q^{4} + 26 q^{5} + 4 q^{7} + 8 q^{8} + 127 q^{9} - 24 q^{10} - 50 q^{11} - 8 q^{12} + 138 q^{13} + 8 q^{14} + 140 q^{15} + 144 q^{16} - 30 q^{17} + 90 q^{18} + 80 q^{19} + 104 q^{20} - 336 q^{21} - 144 q^{22} + 72 q^{23} + 21 q^{25} - 40 q^{26} - 464 q^{27} + 16 q^{28} - 378 q^{29} - 240 q^{30} - 496 q^{31} + 32 q^{32} + 124 q^{33} - 180 q^{34} - 464 q^{35} + 508 q^{36} + 37 q^{37} - 472 q^{38} - 680 q^{39} - 96 q^{40} - 512 q^{41} - 704 q^{42} + 104 q^{43} - 200 q^{44} + 430 q^{45} + 764 q^{46} + 640 q^{47} - 32 q^{48} + 1053 q^{49} - 402 q^{50} + 964 q^{51} + 552 q^{52} - 1178 q^{53} - 480 q^{54} - 584 q^{55} + 32 q^{56} + 736 q^{57} + 712 q^{58} + 2200 q^{59} + 560 q^{60} + 470 q^{61} + 84 q^{62} + 1132 q^{63} + 576 q^{64} - 160 q^{65} - 624 q^{66} + 242 q^{67} - 120 q^{68} + 680 q^{69} + 1320 q^{70} - 1908 q^{71} + 360 q^{72} + 2108 q^{73} + 370 q^{74} + 100 q^{75} + 320 q^{76} - 464 q^{77} - 2076 q^{78} + 1196 q^{79} + 416 q^{80} - 1807 q^{81} - 572 q^{82} + 208 q^{83} - 1344 q^{84} + 2196 q^{85} - 2272 q^{86} - 2508 q^{87} - 576 q^{88} + 1310 q^{89} + 1460 q^{90} + 3844 q^{91} + 288 q^{92} - 648 q^{93} - 768 q^{94} - 1484 q^{95} + 3438 q^{97} + 2898 q^{98} - 5048 q^{99} + O(q^{100}) \)

Decomposition of \(S_{4}^{\mathrm{new}}(\Gamma_0(74))\) into newform subspaces

Label Dim. \(A\) Field CM Traces A-L signs $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$ 2 37
74.4.a.a $1$ $4.366$ \(\Q\) None \(-2\) \(-5\) \(12\) \(-7\) $+$ $-$ \(q-2q^{2}-5q^{3}+4q^{4}+12q^{5}+10q^{6}+\cdots\)
74.4.a.b $1$ $4.366$ \(\Q\) None \(2\) \(-5\) \(-14\) \(-19\) $-$ $+$ \(q+2q^{2}-5q^{3}+4q^{4}-14q^{5}-10q^{6}+\cdots\)
74.4.a.c $3$ $4.366$ 3.3.15629.1 None \(-6\) \(4\) \(7\) \(7\) $+$ $+$ \(q-2q^{2}+(1+\beta _{1}+\beta _{2})q^{3}+4q^{4}+(2+\cdots)q^{5}+\cdots\)
74.4.a.d $4$ $4.366$ \(\mathbb{Q}[x]/(x^{4} - \cdots)\) None \(8\) \(4\) \(21\) \(23\) $-$ $-$ \(q+2q^{2}+(1-\beta _{1})q^{3}+4q^{4}+(5+\beta _{2}+\cdots)q^{5}+\cdots\)

Decomposition of \(S_{4}^{\mathrm{old}}(\Gamma_0(74))\) into lower level spaces

\( S_{4}^{\mathrm{old}}(\Gamma_0(74)) \cong \) \(S_{4}^{\mathrm{new}}(\Gamma_0(37))\)\(^{\oplus 2}\)