Properties

Label 294.4.a
Level $294$
Weight $4$
Character orbit 294.a
Rep. character $\chi_{294}(1,\cdot)$
Character field $\Q$
Dimension $21$
Newform subspaces $15$
Sturm bound $224$
Trace bound $11$

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Defining parameters

Level: \( N \) \(=\) \( 294 = 2 \cdot 3 \cdot 7^{2} \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 294.a (trivial)
Character field: \(\Q\)
Newform subspaces: \( 15 \)
Sturm bound: \(224\)
Trace bound: \(11\)
Distinguishing \(T_p\): \(5\), \(11\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{4}(\Gamma_0(294))\).

Total New Old
Modular forms 184 21 163
Cusp forms 152 21 131
Eisenstein series 32 0 32

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.
\(+\)\(+\)\(+\)\(+\)\(3\)
\(+\)\(+\)\(-\)\(-\)\(2\)
\(+\)\(-\)\(+\)\(-\)\(3\)
\(+\)\(-\)\(-\)\(+\)\(3\)
\(-\)\(+\)\(+\)\(-\)\(2\)
\(-\)\(+\)\(-\)\(+\)\(3\)
\(-\)\(-\)\(+\)\(+\)\(4\)
\(-\)\(-\)\(-\)\(-\)\(1\)
Plus space\(+\)\(13\)
Minus space\(-\)\(8\)

Trace form

\( 21q - 2q^{2} + 3q^{3} + 84q^{4} - 26q^{5} - 6q^{6} - 8q^{8} + 189q^{9} + O(q^{10}) \) \( 21q - 2q^{2} + 3q^{3} + 84q^{4} - 26q^{5} - 6q^{6} - 8q^{8} + 189q^{9} - 28q^{10} + 68q^{11} + 12q^{12} + 38q^{13} + 66q^{15} + 336q^{16} + 122q^{17} - 18q^{18} + 12q^{19} - 104q^{20} + 112q^{22} - 240q^{23} - 24q^{24} + 447q^{25} + 228q^{26} + 27q^{27} - 202q^{29} + 84q^{30} + 104q^{31} - 32q^{32} - 156q^{33} - 260q^{34} + 756q^{36} + 498q^{37} + 104q^{38} + 978q^{39} - 112q^{40} - 510q^{41} + 328q^{43} + 272q^{44} - 234q^{45} + 640q^{46} + 192q^{47} + 48q^{48} + 1506q^{50} - 414q^{51} + 152q^{52} + 1334q^{53} - 54q^{54} + 1240q^{55} + 384q^{57} + 684q^{58} + 1924q^{59} + 264q^{60} + 758q^{61} - 144q^{62} + 1344q^{64} + 316q^{65} - 456q^{66} - 2304q^{67} + 488q^{68} - 264q^{69} - 1864q^{71} - 72q^{72} - 1646q^{73} - 1724q^{74} + 693q^{75} + 48q^{76} + 84q^{78} - 1784q^{79} - 416q^{80} + 1701q^{81} - 852q^{82} - 772q^{83} - 1412q^{85} - 1032q^{86} - 1014q^{87} + 448q^{88} - 1230q^{89} - 252q^{90} - 960q^{92} - 3804q^{93} - 152q^{95} - 96q^{96} + 106q^{97} + 612q^{99} + O(q^{100}) \)

Decomposition of \(S_{4}^{\mathrm{new}}(\Gamma_0(294))\) into newform subspaces

Label Dim. \(A\) Field CM Traces A-L signs $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\) 2 3 7
294.4.a.a \(1\) \(17.347\) \(\Q\) None \(-2\) \(-3\) \(-15\) \(0\) \(+\) \(+\) \(+\) \(q-2q^{2}-3q^{3}+4q^{4}-15q^{5}+6q^{6}+\cdots\)
294.4.a.b \(1\) \(17.347\) \(\Q\) None \(-2\) \(-3\) \(-8\) \(0\) \(+\) \(+\) \(-\) \(q-2q^{2}-3q^{3}+4q^{4}-8q^{5}+6q^{6}+\cdots\)
294.4.a.c \(1\) \(17.347\) \(\Q\) None \(-2\) \(-3\) \(6\) \(0\) \(+\) \(+\) \(-\) \(q-2q^{2}-3q^{3}+4q^{4}+6q^{5}+6q^{6}+\cdots\)
294.4.a.d \(1\) \(17.347\) \(\Q\) None \(-2\) \(3\) \(-6\) \(0\) \(+\) \(-\) \(+\) \(q-2q^{2}+3q^{3}+4q^{4}-6q^{5}-6q^{6}+\cdots\)
294.4.a.e \(1\) \(17.347\) \(\Q\) None \(-2\) \(3\) \(-6\) \(0\) \(+\) \(-\) \(-\) \(q-2q^{2}+3q^{3}+4q^{4}-6q^{5}-6q^{6}+\cdots\)
294.4.a.f \(1\) \(17.347\) \(\Q\) None \(-2\) \(3\) \(8\) \(0\) \(+\) \(-\) \(-\) \(q-2q^{2}+3q^{3}+4q^{4}+8q^{5}-6q^{6}+\cdots\)
294.4.a.g \(1\) \(17.347\) \(\Q\) None \(-2\) \(3\) \(15\) \(0\) \(+\) \(-\) \(-\) \(q-2q^{2}+3q^{3}+4q^{4}+15q^{5}-6q^{6}+\cdots\)
294.4.a.h \(1\) \(17.347\) \(\Q\) None \(2\) \(-3\) \(-2\) \(0\) \(-\) \(+\) \(-\) \(q+2q^{2}-3q^{3}+4q^{4}-2q^{5}-6q^{6}+\cdots\)
294.4.a.i \(1\) \(17.347\) \(\Q\) None \(2\) \(3\) \(-18\) \(0\) \(-\) \(-\) \(-\) \(q+2q^{2}+3q^{3}+4q^{4}-18q^{5}+6q^{6}+\cdots\)
294.4.a.j \(2\) \(17.347\) \(\Q(\sqrt{2}) \) None \(-4\) \(-6\) \(12\) \(0\) \(+\) \(+\) \(+\) \(q-2q^{2}-3q^{3}+4q^{4}+(6+\beta )q^{5}+6q^{6}+\cdots\)
294.4.a.k \(2\) \(17.347\) \(\Q(\sqrt{2}) \) None \(-4\) \(6\) \(-12\) \(0\) \(+\) \(-\) \(+\) \(q-2q^{2}+3q^{3}+4q^{4}+(-6+\beta )q^{5}+\cdots\)
294.4.a.l \(2\) \(17.347\) \(\Q(\sqrt{2}) \) None \(4\) \(-6\) \(-12\) \(0\) \(-\) \(+\) \(+\) \(q+2q^{2}-3q^{3}+4q^{4}+(-6+\beta )q^{5}+\cdots\)
294.4.a.m \(2\) \(17.347\) \(\Q(\sqrt{1345}) \) None \(4\) \(-6\) \(-5\) \(0\) \(-\) \(+\) \(-\) \(q+2q^{2}-3q^{3}+4q^{4}+(-2-\beta )q^{5}+\cdots\)
294.4.a.n \(2\) \(17.347\) \(\Q(\sqrt{1345}) \) None \(4\) \(6\) \(5\) \(0\) \(-\) \(-\) \(+\) \(q+2q^{2}+3q^{3}+4q^{4}+(3-\beta )q^{5}+6q^{6}+\cdots\)
294.4.a.o \(2\) \(17.347\) \(\Q(\sqrt{2}) \) None \(4\) \(6\) \(12\) \(0\) \(-\) \(-\) \(+\) \(q+2q^{2}+3q^{3}+4q^{4}+(6+\beta )q^{5}+6q^{6}+\cdots\)

Decomposition of \(S_{4}^{\mathrm{old}}(\Gamma_0(294))\) into lower level spaces

\( S_{4}^{\mathrm{old}}(\Gamma_0(294)) \cong \) \(S_{4}^{\mathrm{new}}(\Gamma_0(6))\)\(^{\oplus 3}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_0(7))\)\(^{\oplus 8}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_0(14))\)\(^{\oplus 4}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_0(21))\)\(^{\oplus 4}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_0(42))\)\(^{\oplus 2}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_0(49))\)\(^{\oplus 4}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_0(98))\)\(^{\oplus 2}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_0(147))\)\(^{\oplus 2}\)