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Properties

Label 74.6.a
Level $74$
Weight $6$
Character orbit 74.a
Rep. character $\chi_{74}(1,\cdot)$
Character field $\Q$
Dimension $15$
Newform subspaces $5$
Sturm bound $57$
Trace bound $3$

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Defining parameters

Level: \( N \) \(=\) \( 74 = 2 \cdot 37 \)
Weight: \( k \) \(=\) \( 6 \)
Character orbit: \([\chi]\) \(=\) 74.a (trivial)
Character field: \(\Q\)
Newform subspaces: \( 5 \)
Sturm bound: \(57\)
Trace bound: \(3\)
Distinguishing \(T_p\): \(3\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{6}(\Gamma_0(74))\).

Total New Old
Modular forms 49 15 34
Cusp forms 45 15 30
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
\(+\)\(+\)$+$\(3\)
\(+\)\(-\)$-$\(5\)
\(-\)\(+\)$-$\(5\)
\(-\)\(-\)$+$\(2\)
Plus space\(+\)\(5\)
Minus space\(-\)\(10\)

Trace form

\( 15 q - 4 q^{2} + 22 q^{3} + 240 q^{4} - 94 q^{5} + 312 q^{7} - 64 q^{8} + 1177 q^{9} + O(q^{10}) \) \( 15 q - 4 q^{2} + 22 q^{3} + 240 q^{4} - 94 q^{5} + 312 q^{7} - 64 q^{8} + 1177 q^{9} + 496 q^{10} + 262 q^{11} + 352 q^{12} - 982 q^{13} - 880 q^{14} + 728 q^{15} + 3840 q^{16} + 2178 q^{17} - 1620 q^{18} + 1896 q^{19} - 1504 q^{20} + 7716 q^{21} + 1888 q^{22} + 3588 q^{23} + 8511 q^{25} + 7952 q^{26} + 10156 q^{27} + 4992 q^{28} + 4290 q^{29} - 8160 q^{30} - 2236 q^{31} - 1024 q^{32} - 3872 q^{33} + 7656 q^{34} + 1612 q^{35} + 18832 q^{36} - 1369 q^{37} + 9680 q^{38} + 1732 q^{39} + 7936 q^{40} - 27848 q^{41} - 17792 q^{42} - 36416 q^{43} + 4192 q^{44} + 8146 q^{45} - 17160 q^{46} - 55244 q^{47} + 5632 q^{48} + 37383 q^{49} - 30588 q^{50} - 92528 q^{51} - 15712 q^{52} + 50398 q^{53} - 12864 q^{54} - 56060 q^{55} - 14080 q^{56} - 77756 q^{57} - 1616 q^{58} - 27044 q^{59} + 11648 q^{60} - 29454 q^{61} - 51096 q^{62} + 91252 q^{63} + 61440 q^{64} - 56656 q^{65} - 34080 q^{66} - 55258 q^{67} + 34848 q^{68} - 189928 q^{69} + 16 q^{70} + 17496 q^{71} - 25920 q^{72} - 12020 q^{73} - 27380 q^{74} + 364888 q^{75} + 30336 q^{76} + 132388 q^{77} - 31608 q^{78} + 35372 q^{79} - 24064 q^{80} + 27239 q^{81} + 59192 q^{82} - 40484 q^{83} + 123456 q^{84} - 69588 q^{85} + 65792 q^{86} - 95940 q^{87} + 30208 q^{88} - 252970 q^{89} + 42680 q^{90} + 175184 q^{91} + 57408 q^{92} + 510456 q^{93} + 23808 q^{94} - 352796 q^{95} + 75034 q^{97} - 357732 q^{98} + 166744 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{6}^{\mathrm{new}}(\Gamma_0(74))\) into newform subspaces

Label Char Prim Dim $A$ Field CM Traces A-L signs Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$ 2 37
74.6.a.a 74.a 1.a $1$ $11.868$ \(\Q\) None \(4\) \(-15\) \(4\) \(15\) $-$ $-$ $\mathrm{SU}(2)$ \(q+4q^{2}-15q^{3}+2^{4}q^{4}+4q^{5}-60q^{6}+\cdots\)
74.6.a.b 74.a 1.a $1$ $11.868$ \(\Q\) None \(4\) \(7\) \(-84\) \(-139\) $-$ $-$ $\mathrm{SU}(2)$ \(q+4q^{2}+7q^{3}+2^{4}q^{4}-84q^{5}+28q^{6}+\cdots\)
74.6.a.c 74.a 1.a $3$ $11.868$ 3.3.324233.1 None \(-12\) \(-8\) \(-42\) \(84\) $+$ $+$ $\mathrm{SU}(2)$ \(q-4q^{2}+(-3+\beta _{1}-\beta _{2})q^{3}+2^{4}q^{4}+\cdots\)
74.6.a.d 74.a 1.a $5$ $11.868$ \(\mathbb{Q}[x]/(x^{5} - \cdots)\) None \(-20\) \(19\) \(-67\) \(182\) $+$ $-$ $\mathrm{SU}(2)$ \(q-4q^{2}+(4+\beta _{2})q^{3}+2^{4}q^{4}+(-14+\cdots)q^{5}+\cdots\)
74.6.a.e 74.a 1.a $5$ $11.868$ \(\mathbb{Q}[x]/(x^{5} - \cdots)\) None \(20\) \(19\) \(95\) \(170\) $-$ $+$ $\mathrm{SU}(2)$ \(q+4q^{2}+(4-\beta _{1})q^{3}+2^{4}q^{4}+(19+\beta _{2}+\cdots)q^{5}+\cdots\)

Decomposition of \(S_{6}^{\mathrm{old}}(\Gamma_0(74))\) into lower level spaces

\( S_{6}^{\mathrm{old}}(\Gamma_0(74)) \cong \) \(S_{6}^{\mathrm{new}}(\Gamma_0(37))\)\(^{\oplus 2}\)