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Properties

Label 294.2.a
Level $294$
Weight $2$
Character orbit 294.a
Rep. character $\chi_{294}(1,\cdot)$
Character field $\Q$
Dimension $7$
Newform subspaces $7$
Sturm bound $112$
Trace bound $5$

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Defining parameters

Level: \( N \) \(=\) \( 294 = 2 \cdot 3 \cdot 7^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 294.a (trivial)
Character field: \(\Q\)
Newform subspaces: \( 7 \)
Sturm bound: \(112\)
Trace bound: \(5\)
Distinguishing \(T_p\): \(5\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_0(294))\).

Total New Old
Modular forms 72 7 65
Cusp forms 41 7 34
Eisenstein series 31 0 31

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

\(2\)\(3\)\(7\)FrickeDim
\(+\)\(+\)\(-\)$-$\(2\)
\(+\)\(-\)\(+\)$-$\(1\)
\(+\)\(-\)\(-\)$+$\(1\)
\(-\)\(+\)\(+\)$-$\(1\)
\(-\)\(-\)\(-\)$-$\(2\)
Plus space\(+\)\(1\)
Minus space\(-\)\(6\)

Trace form

\( 7 q - q^{2} + q^{3} + 7 q^{4} + 2 q^{5} + q^{6} - q^{8} + 7 q^{9} + O(q^{10}) \) \( 7 q - q^{2} + q^{3} + 7 q^{4} + 2 q^{5} + q^{6} - q^{8} + 7 q^{9} + 2 q^{10} + 4 q^{11} + q^{12} - 6 q^{13} - 2 q^{15} + 7 q^{16} - 2 q^{17} - q^{18} + 4 q^{19} + 2 q^{20} + 8 q^{22} + q^{24} + 21 q^{25} - 6 q^{26} + q^{27} + 10 q^{29} + 2 q^{30} - q^{32} - 4 q^{33} - 2 q^{34} + 7 q^{36} - 14 q^{37} + 4 q^{38} - 22 q^{39} + 2 q^{40} + 6 q^{41} - 12 q^{43} + 4 q^{44} + 2 q^{45} + q^{48} - 39 q^{50} + 6 q^{51} - 6 q^{52} - 38 q^{53} + q^{54} - 8 q^{55} - 28 q^{57} - 34 q^{58} - 4 q^{59} - 2 q^{60} - 6 q^{61} + 7 q^{64} - 4 q^{65} - 4 q^{66} - 12 q^{67} - 2 q^{68} + 8 q^{69} + 16 q^{71} - q^{72} - 10 q^{73} - 22 q^{74} - q^{75} + 4 q^{76} + 10 q^{78} - 12 q^{79} + 2 q^{80} + 7 q^{81} + 6 q^{82} + 4 q^{83} - 12 q^{85} + 12 q^{86} - 2 q^{87} + 8 q^{88} + 6 q^{89} + 2 q^{90} - 24 q^{93} + 32 q^{95} + q^{96} + 14 q^{97} + 4 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(294))\) 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 7
294.2.a.a 294.a 1.a $1$ $2.348$ \(\Q\) None \(-1\) \(-1\) \(-3\) \(0\) $+$ $+$ $-$ $\mathrm{SU}(2)$ \(q-q^{2}-q^{3}+q^{4}-3q^{5}+q^{6}-q^{8}+\cdots\)
294.2.a.b 294.a 1.a $1$ $2.348$ \(\Q\) None \(-1\) \(-1\) \(4\) \(0\) $+$ $+$ $-$ $\mathrm{SU}(2)$ \(q-q^{2}-q^{3}+q^{4}+4q^{5}+q^{6}-q^{8}+\cdots\)
294.2.a.c 294.a 1.a $1$ $2.348$ \(\Q\) None \(-1\) \(1\) \(-4\) \(0\) $+$ $-$ $-$ $\mathrm{SU}(2)$ \(q-q^{2}+q^{3}+q^{4}-4q^{5}-q^{6}-q^{8}+\cdots\)
294.2.a.d 294.a 1.a $1$ $2.348$ \(\Q\) None \(-1\) \(1\) \(3\) \(0\) $+$ $-$ $+$ $\mathrm{SU}(2)$ \(q-q^{2}+q^{3}+q^{4}+3q^{5}-q^{6}-q^{8}+\cdots\)
294.2.a.e 294.a 1.a $1$ $2.348$ \(\Q\) None \(1\) \(-1\) \(1\) \(0\) $-$ $+$ $+$ $\mathrm{SU}(2)$ \(q+q^{2}-q^{3}+q^{4}+q^{5}-q^{6}+q^{8}+\cdots\)
294.2.a.f 294.a 1.a $1$ $2.348$ \(\Q\) None \(1\) \(1\) \(-1\) \(0\) $-$ $-$ $-$ $\mathrm{SU}(2)$ \(q+q^{2}+q^{3}+q^{4}-q^{5}+q^{6}+q^{8}+\cdots\)
294.2.a.g 294.a 1.a $1$ $2.348$ \(\Q\) None \(1\) \(1\) \(2\) \(0\) $-$ $-$ $-$ $\mathrm{SU}(2)$ \(q+q^{2}+q^{3}+q^{4}+2q^{5}+q^{6}+q^{8}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_0(294))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_0(294)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_0(14))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(21))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(42))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(49))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(98))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(147))\)\(^{\oplus 2}\)