Properties

Label 74.8.a
Level $74$
Weight $8$
Character orbit 74.a
Rep. character $\chi_{74}(1,\cdot)$
Character field $\Q$
Dimension $21$
Newform subspaces $4$
Sturm bound $76$
Trace bound $2$

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Defining parameters

Level: \( N \) \(=\) \( 74 = 2 \cdot 37 \)
Weight: \( k \) \(=\) \( 8 \)
Character orbit: \([\chi]\) \(=\) 74.a (trivial)
Character field: \(\Q\)
Newform subspaces: \( 4 \)
Sturm bound: \(76\)
Trace bound: \(2\)
Distinguishing \(T_p\): \(3\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{8}(\Gamma_0(74))\).

Total New Old
Modular forms 69 21 48
Cusp forms 65 21 44
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
\(+\)\(+\)\(+\)\(6\)
\(+\)\(-\)\(-\)\(4\)
\(-\)\(+\)\(-\)\(4\)
\(-\)\(-\)\(+\)\(7\)
Plus space\(+\)\(13\)
Minus space\(-\)\(8\)

Trace form

\( 21 q + 8 q^{2} - 26 q^{3} + 1344 q^{4} + 246 q^{5} + 192 q^{6} - 2136 q^{7} + 512 q^{8} + 17995 q^{9} + O(q^{10}) \) \( 21 q + 8 q^{2} - 26 q^{3} + 1344 q^{4} + 246 q^{5} + 192 q^{6} - 2136 q^{7} + 512 q^{8} + 17995 q^{9} + 416 q^{10} - 1818 q^{11} - 1664 q^{12} + 4798 q^{13} + 25248 q^{14} + 18920 q^{15} + 86016 q^{16} - 21690 q^{17} - 61848 q^{18} - 16704 q^{19} + 15744 q^{20} - 19908 q^{21} + 11648 q^{22} + 87476 q^{23} + 12288 q^{24} + 385581 q^{25} - 125472 q^{26} - 50180 q^{27} - 136704 q^{28} + 285654 q^{29} + 310080 q^{30} + 111556 q^{31} + 32768 q^{32} + 901312 q^{33} + 177456 q^{34} + 513116 q^{35} + 1151680 q^{36} + 50653 q^{37} - 700992 q^{38} - 496796 q^{39} + 26624 q^{40} - 163120 q^{41} + 896128 q^{42} + 3933272 q^{43} - 116352 q^{44} + 2387110 q^{45} - 22704 q^{46} - 301148 q^{47} - 106496 q^{48} + 835101 q^{49} + 2179128 q^{50} - 2368592 q^{51} + 307072 q^{52} + 2381818 q^{53} - 490944 q^{54} - 1834924 q^{55} + 1615872 q^{56} + 835852 q^{57} - 74848 q^{58} - 1989660 q^{59} + 1210880 q^{60} - 5609946 q^{61} + 2264304 q^{62} - 3434540 q^{63} + 5505024 q^{64} + 1519280 q^{65} - 4625088 q^{66} + 2890918 q^{67} - 1388160 q^{68} - 10217032 q^{69} - 11807200 q^{70} + 1851912 q^{71} - 3958272 q^{72} + 8415164 q^{73} + 2026120 q^{74} - 8186600 q^{75} - 1069056 q^{76} - 31574388 q^{77} + 4882128 q^{78} + 1414636 q^{79} + 1007616 q^{80} + 8717021 q^{81} - 8778608 q^{82} - 23694852 q^{83} - 1274112 q^{84} - 8432844 q^{85} - 9178208 q^{86} + 8689068 q^{87} + 745472 q^{88} + 43803746 q^{89} + 6211280 q^{90} - 30395504 q^{91} + 5598464 q^{92} - 8919288 q^{93} + 6820992 q^{94} - 22573244 q^{95} + 786432 q^{96} - 3178498 q^{97} - 7048504 q^{98} + 8248312 q^{99} + O(q^{100}) \)

Decomposition of \(S_{8}^{\mathrm{new}}(\Gamma_0(74))\) into newform subspaces

Label Char Prim Dim $A$ Field CM Minimal twist Traces A-L signs Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$ 2 37
74.8.a.a 74.a 1.a $4$ $23.116$ \(\mathbb{Q}[x]/(x^{4} - \cdots)\) None 74.8.a.a \(-32\) \(-53\) \(111\) \(-1666\) $+$ $-$ $\mathrm{SU}(2)$ \(q-8q^{2}+(-14+2\beta _{1}+\beta _{3})q^{3}+2^{6}q^{4}+\cdots\)
74.8.a.b 74.a 1.a $4$ $23.116$ \(\mathbb{Q}[x]/(x^{4} - \cdots)\) None 74.8.a.b \(32\) \(-41\) \(-363\) \(-774\) $-$ $+$ $\mathrm{SU}(2)$ \(q+8q^{2}+(-10+\beta _{2})q^{3}+2^{6}q^{4}+(-89+\cdots)q^{5}+\cdots\)
74.8.a.c 74.a 1.a $6$ $23.116$ \(\mathbb{Q}[x]/(x^{6} - \cdots)\) None 74.8.a.c \(-48\) \(28\) \(-14\) \(-980\) $+$ $+$ $\mathrm{SU}(2)$ \(q-8q^{2}+(5-\beta _{1})q^{3}+2^{6}q^{4}+(-4+\cdots)q^{5}+\cdots\)
74.8.a.d 74.a 1.a $7$ $23.116$ \(\mathbb{Q}[x]/(x^{7} - \cdots)\) None 74.8.a.d \(56\) \(40\) \(512\) \(1284\) $-$ $-$ $\mathrm{SU}(2)$ \(q+8q^{2}+(6-\beta _{1})q^{3}+2^{6}q^{4}+(74-2\beta _{1}+\cdots)q^{5}+\cdots\)

Decomposition of \(S_{8}^{\mathrm{old}}(\Gamma_0(74))\) into lower level spaces

\( S_{8}^{\mathrm{old}}(\Gamma_0(74)) \simeq \) \(S_{8}^{\mathrm{new}}(\Gamma_0(2))\)\(^{\oplus 2}\)\(\oplus\)\(S_{8}^{\mathrm{new}}(\Gamma_0(37))\)\(^{\oplus 2}\)