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Properties

Label 3174.2.a
Level $3174$
Weight $2$
Character orbit 3174.a
Rep. character $\chi_{3174}(1,\cdot)$
Character field $\Q$
Dimension $83$
Newform subspaces $30$
Sturm bound $1104$
Trace bound $25$

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Defining parameters

Level: \( N \) \(=\) \( 3174 = 2 \cdot 3 \cdot 23^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 3174.a (trivial)
Character field: \(\Q\)
Newform subspaces: \( 30 \)
Sturm bound: \(1104\)
Trace bound: \(25\)
Distinguishing \(T_p\): \(5\), \(7\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_0(3174))\).

Total New Old
Modular forms 600 83 517
Cusp forms 505 83 422
Eisenstein series 95 0 95

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

\(2\)\(3\)\(23\)FrickeDim.
\(+\)\(+\)\(+\)\(+\)\(7\)
\(+\)\(+\)\(-\)\(-\)\(14\)
\(+\)\(-\)\(+\)\(-\)\(11\)
\(+\)\(-\)\(-\)\(+\)\(10\)
\(-\)\(+\)\(+\)\(-\)\(13\)
\(-\)\(+\)\(-\)\(+\)\(8\)
\(-\)\(-\)\(+\)\(+\)\(5\)
\(-\)\(-\)\(-\)\(-\)\(15\)
Plus space\(+\)\(30\)
Minus space\(-\)\(53\)

Trace form

\( 83 q - q^{2} - q^{3} + 83 q^{4} + 2 q^{5} - q^{6} - q^{8} + 83 q^{9} + O(q^{10}) \) \( 83 q - q^{2} - q^{3} + 83 q^{4} + 2 q^{5} - q^{6} - q^{8} + 83 q^{9} - 2 q^{10} + 12 q^{11} - q^{12} + 2 q^{13} + 2 q^{15} + 83 q^{16} + 6 q^{17} - q^{18} + 8 q^{19} + 2 q^{20} - 4 q^{21} - q^{24} + 93 q^{25} + 2 q^{26} - q^{27} + 10 q^{29} + 6 q^{30} + 8 q^{31} - q^{32} + 6 q^{34} + 24 q^{35} + 83 q^{36} - 10 q^{37} + 12 q^{38} - 6 q^{39} - 2 q^{40} - 2 q^{41} + 4 q^{42} + 16 q^{43} + 12 q^{44} + 2 q^{45} - q^{48} + 83 q^{49} + q^{50} + 10 q^{51} + 2 q^{52} - 22 q^{53} - q^{54} - 8 q^{57} + 2 q^{58} + 12 q^{59} + 2 q^{60} - 2 q^{61} + 16 q^{62} + 83 q^{64} - 20 q^{65} + 12 q^{66} - 16 q^{67} + 6 q^{68} + 32 q^{70} + 16 q^{71} - q^{72} + 22 q^{73} - 30 q^{74} + q^{75} + 8 q^{76} - 32 q^{77} + 10 q^{78} + 8 q^{79} + 2 q^{80} + 83 q^{81} + 6 q^{82} - 20 q^{83} - 4 q^{84} + 4 q^{85} - 4 q^{86} + 10 q^{87} - 18 q^{89} - 2 q^{90} + 32 q^{91} - 16 q^{94} - 8 q^{95} - q^{96} + 14 q^{97} - 25 q^{98} + 12 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(3174))\) 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 3 23
3174.2.a.a 3174.a 1.a $1$ $25.345$ \(\Q\) None \(-1\) \(-1\) \(-2\) \(-5\) $+$ $+$ $-$ $\mathrm{SU}(2)$ \(q-q^{2}-q^{3}+q^{4}-2q^{5}+q^{6}-5q^{7}+\cdots\)
3174.2.a.b 3174.a 1.a $1$ $25.345$ \(\Q\) None \(-1\) \(-1\) \(2\) \(2\) $+$ $+$ $-$ $\mathrm{SU}(2)$ \(q-q^{2}-q^{3}+q^{4}+2q^{5}+q^{6}+2q^{7}+\cdots\)
3174.2.a.c 3174.a 1.a $1$ $25.345$ \(\Q\) None \(-1\) \(-1\) \(2\) \(5\) $+$ $+$ $-$ $\mathrm{SU}(2)$ \(q-q^{2}-q^{3}+q^{4}+2q^{5}+q^{6}+5q^{7}+\cdots\)
3174.2.a.d 3174.a 1.a $1$ $25.345$ \(\Q\) None \(-1\) \(1\) \(0\) \(-2\) $+$ $-$ $-$ $\mathrm{SU}(2)$ \(q-q^{2}+q^{3}+q^{4}-q^{6}-2q^{7}-q^{8}+\cdots\)
3174.2.a.e 3174.a 1.a $1$ $25.345$ \(\Q\) None \(1\) \(-1\) \(-2\) \(0\) $-$ $+$ $-$ $\mathrm{SU}(2)$ \(q+q^{2}-q^{3}+q^{4}-2q^{5}-q^{6}+q^{8}+\cdots\)
3174.2.a.f 3174.a 1.a $1$ $25.345$ \(\Q\) None \(1\) \(-1\) \(-1\) \(0\) $-$ $+$ $-$ $\mathrm{SU}(2)$ \(q+q^{2}-q^{3}+q^{4}-q^{5}-q^{6}+q^{8}+\cdots\)
3174.2.a.g 3174.a 1.a $1$ $25.345$ \(\Q\) None \(1\) \(-1\) \(1\) \(0\) $-$ $+$ $-$ $\mathrm{SU}(2)$ \(q+q^{2}-q^{3}+q^{4}+q^{5}-q^{6}+q^{8}+\cdots\)
3174.2.a.h 3174.a 1.a $2$ $25.345$ \(\Q(\sqrt{2}) \) None \(-2\) \(-2\) \(0\) \(0\) $+$ $+$ $+$ $\mathrm{SU}(2)$ \(q-q^{2}-q^{3}+q^{4}+q^{6}+\beta q^{7}-q^{8}+\cdots\)
3174.2.a.i 3174.a 1.a $2$ $25.345$ \(\Q(\sqrt{2}) \) None \(-2\) \(-2\) \(0\) \(0\) $+$ $+$ $-$ $\mathrm{SU}(2)$ \(q-q^{2}-q^{3}+q^{4}+\beta q^{5}+q^{6}-\beta q^{7}+\cdots\)
3174.2.a.j 3174.a 1.a $2$ $25.345$ \(\Q(\sqrt{3}) \) None \(-2\) \(2\) \(0\) \(0\) $+$ $-$ $-$ $\mathrm{SU}(2)$ \(q-q^{2}+q^{3}+q^{4}+\beta q^{5}-q^{6}-q^{8}+\cdots\)
3174.2.a.k 3174.a 1.a $2$ $25.345$ \(\Q(\sqrt{6}) \) None \(-2\) \(2\) \(0\) \(0\) $+$ $-$ $-$ $\mathrm{SU}(2)$ \(q-q^{2}+q^{3}+q^{4}-q^{6}+\beta q^{7}-q^{8}+\cdots\)
3174.2.a.l 3174.a 1.a $2$ $25.345$ \(\Q(\sqrt{2}) \) None \(-2\) \(2\) \(0\) \(0\) $+$ $-$ $+$ $\mathrm{SU}(2)$ \(q-q^{2}+q^{3}+q^{4}+\beta q^{5}-q^{6}+3\beta q^{7}+\cdots\)
3174.2.a.m 3174.a 1.a $2$ $25.345$ \(\Q(\sqrt{2}) \) None \(2\) \(-2\) \(0\) \(0\) $-$ $+$ $+$ $\mathrm{SU}(2)$ \(q+q^{2}-q^{3}+q^{4}+3\beta q^{5}-q^{6}+\beta q^{7}+\cdots\)
3174.2.a.n 3174.a 1.a $2$ $25.345$ \(\Q(\sqrt{2}) \) None \(2\) \(-2\) \(0\) \(0\) $-$ $+$ $+$ $\mathrm{SU}(2)$ \(q+q^{2}-q^{3}+q^{4}+2\beta q^{5}-q^{6}-\beta q^{7}+\cdots\)
3174.2.a.o 3174.a 1.a $2$ $25.345$ \(\Q(\sqrt{41}) \) None \(2\) \(2\) \(-1\) \(-3\) $-$ $-$ $-$ $\mathrm{SU}(2)$ \(q+q^{2}+q^{3}+q^{4}-\beta q^{5}+q^{6}+(-1+\cdots)q^{7}+\cdots\)
3174.2.a.p 3174.a 1.a $2$ $25.345$ \(\Q(\sqrt{3}) \) None \(2\) \(2\) \(0\) \(0\) $-$ $-$ $-$ $\mathrm{SU}(2)$ \(q+q^{2}+q^{3}+q^{4}+\beta q^{5}+q^{6}+q^{8}+\cdots\)
3174.2.a.q 3174.a 1.a $2$ $25.345$ \(\Q(\sqrt{3}) \) None \(2\) \(2\) \(0\) \(0\) $-$ $-$ $-$ $\mathrm{SU}(2)$ \(q+q^{2}+q^{3}+q^{4}+q^{6}-\beta q^{7}+q^{8}+\cdots\)
3174.2.a.r 3174.a 1.a $2$ $25.345$ \(\Q(\sqrt{41}) \) None \(2\) \(2\) \(1\) \(3\) $-$ $-$ $-$ $\mathrm{SU}(2)$ \(q+q^{2}+q^{3}+q^{4}+\beta q^{5}+q^{6}+(1+\beta )q^{7}+\cdots\)
3174.2.a.s 3174.a 1.a $2$ $25.345$ \(\Q(\sqrt{5}) \) None \(2\) \(2\) \(2\) \(0\) $-$ $-$ $-$ $\mathrm{SU}(2)$ \(q+q^{2}+q^{3}+q^{4}+(1+\beta )q^{5}+q^{6}+\cdots\)
3174.2.a.t 3174.a 1.a $4$ $25.345$ \(\Q(\sqrt{3}, \sqrt{35})\) None \(-4\) \(-4\) \(0\) \(0\) $+$ $+$ $-$ $\mathrm{SU}(2)$ \(q-q^{2}-q^{3}+q^{4}+\beta _{1}q^{5}+q^{6}+(-\beta _{1}+\cdots)q^{7}+\cdots\)
3174.2.a.u 3174.a 1.a $4$ $25.345$ \(\Q(\zeta_{24})^+\) None \(-4\) \(4\) \(0\) \(0\) $+$ $-$ $+$ $\mathrm{SU}(2)$ \(q-q^{2}+q^{3}+q^{4}+(-\beta _{1}-\beta _{3})q^{5}+\cdots\)
3174.2.a.v 3174.a 1.a $4$ $25.345$ \(\Q(\zeta_{24})^+\) None \(4\) \(-4\) \(0\) \(0\) $-$ $+$ $+$ $\mathrm{SU}(2)$ \(q+q^{2}-q^{3}+q^{4}+(-\beta _{1}-\beta _{3})q^{5}+\cdots\)
3174.2.a.w 3174.a 1.a $5$ $25.345$ \(\Q(\zeta_{22})^+\) None \(-5\) \(-5\) \(-1\) \(-1\) $+$ $+$ $-$ $\mathrm{SU}(2)$ \(q-q^{2}-q^{3}+q^{4}+(\beta _{2}-\beta _{3}-\beta _{4})q^{5}+\cdots\)
3174.2.a.x 3174.a 1.a $5$ $25.345$ \(\Q(\zeta_{22})^+\) None \(-5\) \(-5\) \(1\) \(1\) $+$ $+$ $+$ $\mathrm{SU}(2)$ \(q-q^{2}-q^{3}+q^{4}+(\beta _{1}+\beta _{2}-\beta _{4})q^{5}+\cdots\)
3174.2.a.y 3174.a 1.a $5$ $25.345$ \(\Q(\zeta_{22})^+\) None \(-5\) \(5\) \(-11\) \(1\) $+$ $-$ $-$ $\mathrm{SU}(2)$ \(q-q^{2}+q^{3}+q^{4}+(-3-\beta _{2}+2\beta _{3}+\cdots)q^{5}+\cdots\)
3174.2.a.z 3174.a 1.a $5$ $25.345$ \(\Q(\zeta_{22})^+\) None \(-5\) \(5\) \(11\) \(-1\) $+$ $-$ $+$ $\mathrm{SU}(2)$ \(q-q^{2}+q^{3}+q^{4}+(2-\beta _{1}-\beta _{2}-\beta _{4})q^{5}+\cdots\)
3174.2.a.ba 3174.a 1.a $5$ $25.345$ \(\Q(\zeta_{22})^+\) None \(5\) \(-5\) \(-1\) \(11\) $-$ $+$ $+$ $\mathrm{SU}(2)$ \(q+q^{2}-q^{3}+q^{4}+(\beta _{2}+\beta _{3}+\beta _{4})q^{5}+\cdots\)
3174.2.a.bb 3174.a 1.a $5$ $25.345$ \(\Q(\zeta_{22})^+\) None \(5\) \(-5\) \(1\) \(-11\) $-$ $+$ $-$ $\mathrm{SU}(2)$ \(q+q^{2}-q^{3}+q^{4}+(1-2\beta _{1}+\beta _{2}+\beta _{4})q^{5}+\cdots\)
3174.2.a.bc 3174.a 1.a $5$ $25.345$ \(\Q(\zeta_{22})^+\) None \(5\) \(5\) \(-7\) \(-7\) $-$ $-$ $+$ $\mathrm{SU}(2)$ \(q+q^{2}+q^{3}+q^{4}+(-1-\beta _{3}+\beta _{4})q^{5}+\cdots\)
3174.2.a.bd 3174.a 1.a $5$ $25.345$ \(\Q(\zeta_{22})^+\) None \(5\) \(5\) \(7\) \(7\) $-$ $-$ $-$ $\mathrm{SU}(2)$ \(q+q^{2}+q^{3}+q^{4}+(1+\beta _{3}-\beta _{4})q^{5}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_0(3174))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_0(3174)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_0(23))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(46))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(69))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(138))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(529))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(1058))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(1587))\)\(^{\oplus 2}\)