Properties

Label 294.6.a
Level $294$
Weight $6$
Character orbit 294.a
Rep. character $\chi_{294}(1,\cdot)$
Character field $\Q$
Dimension $33$
Newform subspaces $23$
Sturm bound $336$
Trace bound $11$

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Defining parameters

Level: \( N \) \(=\) \( 294 = 2 \cdot 3 \cdot 7^{2} \)
Weight: \( k \) \(=\) \( 6 \)
Character orbit: \([\chi]\) \(=\) 294.a (trivial)
Character field: \(\Q\)
Newform subspaces: \( 23 \)
Sturm bound: \(336\)
Trace bound: \(11\)
Distinguishing \(T_p\): \(5\), \(11\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{6}(\Gamma_0(294))\).

Total New Old
Modular forms 296 33 263
Cusp forms 264 33 231
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.
\(+\)\(+\)\(+\)\(+\)\(3\)
\(+\)\(+\)\(-\)\(-\)\(5\)
\(+\)\(-\)\(+\)\(-\)\(4\)
\(+\)\(-\)\(-\)\(+\)\(4\)
\(-\)\(+\)\(+\)\(-\)\(4\)
\(-\)\(+\)\(-\)\(+\)\(4\)
\(-\)\(-\)\(+\)\(+\)\(3\)
\(-\)\(-\)\(-\)\(-\)\(6\)
Plus space\(+\)\(14\)
Minus space\(-\)\(19\)

Trace form

\( 33q + 4q^{2} + 9q^{3} + 528q^{4} + 22q^{5} + 36q^{6} + 64q^{8} + 2673q^{9} + O(q^{10}) \) \( 33q + 4q^{2} + 9q^{3} + 528q^{4} + 22q^{5} + 36q^{6} + 64q^{8} + 2673q^{9} - 360q^{10} - 652q^{11} + 144q^{12} + 694q^{13} + 198q^{15} + 8448q^{16} - 1054q^{17} + 324q^{18} + 3124q^{19} + 352q^{20} - 1696q^{22} + 5424q^{23} + 576q^{24} + 24427q^{25} - 4392q^{26} + 729q^{27} + 1262q^{29} - 5976q^{30} + 616q^{31} + 1024q^{32} + 180q^{33} + 13704q^{34} + 42768q^{36} - 31658q^{37} + 2192q^{38} - 10134q^{39} - 5760q^{40} - 20742q^{41} + 3684q^{43} - 10432q^{44} + 1782q^{45} + 14080q^{46} + 13776q^{47} + 2304q^{48} - 89124q^{50} + 11718q^{51} + 11104q^{52} - 63538q^{53} + 2916q^{54} - 69672q^{55} + 80100q^{57} + 2440q^{58} - 80900q^{59} + 3168q^{60} + 86566q^{61} + 106848q^{62} + 135168q^{64} + 146500q^{65} + 37008q^{66} + 123956q^{67} - 16864q^{68} - 88920q^{69} + 161888q^{71} + 5184q^{72} + 105274q^{73} + 349528q^{74} + 48807q^{75} + 49984q^{76} - 48024q^{78} + 212748q^{79} + 5632q^{80} + 216513q^{81} + 13800q^{82} + 62612q^{83} + 158524q^{85} - 172368q^{86} + 188982q^{87} - 27136q^{88} - 121398q^{89} - 29160q^{90} + 86784q^{92} + 235656q^{93} + 129024q^{94} + 302848q^{95} + 9216q^{96} - 163646q^{97} - 52812q^{99} + O(q^{100}) \)

Decomposition of \(S_{6}^{\mathrm{new}}(\Gamma_0(294))\) 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
294.6.a.a \(1\) \(47.153\) \(\Q\) None \(-4\) \(-9\) \(-26\) \(0\) \(+\) \(+\) \(-\) \(q-4q^{2}-9q^{3}+2^{4}q^{4}-26q^{5}+6^{2}q^{6}+\cdots\)
294.6.a.b \(1\) \(47.153\) \(\Q\) None \(-4\) \(-9\) \(-26\) \(0\) \(+\) \(+\) \(-\) \(q-4q^{2}-9q^{3}+2^{4}q^{4}-26q^{5}+6^{2}q^{6}+\cdots\)
294.6.a.c \(1\) \(47.153\) \(\Q\) None \(-4\) \(-9\) \(72\) \(0\) \(+\) \(+\) \(-\) \(q-4q^{2}-9q^{3}+2^{4}q^{4}+72q^{5}+6^{2}q^{6}+\cdots\)
294.6.a.d \(1\) \(47.153\) \(\Q\) None \(-4\) \(-9\) \(86\) \(0\) \(+\) \(+\) \(+\) \(q-4q^{2}-9q^{3}+2^{4}q^{4}+86q^{5}+6^{2}q^{6}+\cdots\)
294.6.a.e \(1\) \(47.153\) \(\Q\) None \(-4\) \(9\) \(-86\) \(0\) \(+\) \(-\) \(-\) \(q-4q^{2}+9q^{3}+2^{4}q^{4}-86q^{5}-6^{2}q^{6}+\cdots\)
294.6.a.f \(1\) \(47.153\) \(\Q\) None \(-4\) \(9\) \(-44\) \(0\) \(+\) \(-\) \(-\) \(q-4q^{2}+9q^{3}+2^{4}q^{4}-44q^{5}-6^{2}q^{6}+\cdots\)
294.6.a.g \(1\) \(47.153\) \(\Q\) None \(-4\) \(9\) \(26\) \(0\) \(+\) \(-\) \(-\) \(q-4q^{2}+9q^{3}+2^{4}q^{4}+26q^{5}-6^{2}q^{6}+\cdots\)
294.6.a.h \(1\) \(47.153\) \(\Q\) None \(-4\) \(9\) \(54\) \(0\) \(+\) \(-\) \(-\) \(q-4q^{2}+9q^{3}+2^{4}q^{4}+54q^{5}-6^{2}q^{6}+\cdots\)
294.6.a.i \(1\) \(47.153\) \(\Q\) None \(4\) \(-9\) \(-24\) \(0\) \(-\) \(+\) \(-\) \(q+4q^{2}-9q^{3}+2^{4}q^{4}-24q^{5}-6^{2}q^{6}+\cdots\)
294.6.a.j \(1\) \(47.153\) \(\Q\) None \(4\) \(-9\) \(6\) \(0\) \(-\) \(+\) \(-\) \(q+4q^{2}-9q^{3}+2^{4}q^{4}+6q^{5}-6^{2}q^{6}+\cdots\)
294.6.a.k \(1\) \(47.153\) \(\Q\) None \(4\) \(9\) \(-76\) \(0\) \(-\) \(-\) \(-\) \(q+4q^{2}+9q^{3}+2^{4}q^{4}-76q^{5}+6^{2}q^{6}+\cdots\)
294.6.a.l \(1\) \(47.153\) \(\Q\) None \(4\) \(9\) \(-6\) \(0\) \(-\) \(-\) \(+\) \(q+4q^{2}+9q^{3}+2^{4}q^{4}-6q^{5}+6^{2}q^{6}+\cdots\)
294.6.a.m \(1\) \(47.153\) \(\Q\) None \(4\) \(9\) \(66\) \(0\) \(-\) \(-\) \(-\) \(q+4q^{2}+9q^{3}+2^{4}q^{4}+66q^{5}+6^{2}q^{6}+\cdots\)
294.6.a.n \(2\) \(47.153\) \(\Q(\sqrt{2}) \) None \(-8\) \(-18\) \(-108\) \(0\) \(+\) \(+\) \(+\) \(q-4q^{2}-9q^{3}+2^{4}q^{4}+(-54+5\beta )q^{5}+\cdots\)
294.6.a.o \(2\) \(47.153\) \(\Q(\sqrt{505}) \) None \(-8\) \(-18\) \(-17\) \(0\) \(+\) \(+\) \(-\) \(q-4q^{2}-9q^{3}+2^{4}q^{4}+(-9-\beta )q^{5}+\cdots\)
294.6.a.p \(2\) \(47.153\) \(\Q(\sqrt{505}) \) None \(-8\) \(18\) \(17\) \(0\) \(+\) \(-\) \(+\) \(q-4q^{2}+9q^{3}+2^{4}q^{4}+(9+\beta )q^{5}+\cdots\)
294.6.a.q \(2\) \(47.153\) \(\Q(\sqrt{2}) \) None \(-8\) \(18\) \(108\) \(0\) \(+\) \(-\) \(+\) \(q-4q^{2}+9q^{3}+2^{4}q^{4}+(54+5\beta )q^{5}+\cdots\)
294.6.a.r \(2\) \(47.153\) \(\Q(\sqrt{9601}) \) None \(8\) \(-18\) \(-53\) \(0\) \(-\) \(+\) \(+\) \(q+4q^{2}-9q^{3}+2^{4}q^{4}+(-26-\beta )q^{5}+\cdots\)
294.6.a.s \(2\) \(47.153\) \(\Q(\sqrt{4705}) \) None \(8\) \(-18\) \(-18\) \(0\) \(-\) \(+\) \(-\) \(q+4q^{2}-9q^{3}+2^{4}q^{4}+(-9-\beta )q^{5}+\cdots\)
294.6.a.t \(2\) \(47.153\) \(\Q(\sqrt{2}) \) None \(8\) \(-18\) \(108\) \(0\) \(-\) \(+\) \(+\) \(q+4q^{2}-9q^{3}+2^{4}q^{4}+(54+5\beta )q^{5}+\cdots\)
294.6.a.u \(2\) \(47.153\) \(\Q(\sqrt{2}) \) None \(8\) \(18\) \(-108\) \(0\) \(-\) \(-\) \(+\) \(q+4q^{2}+9q^{3}+2^{4}q^{4}+(-54+5\beta )q^{5}+\cdots\)
294.6.a.v \(2\) \(47.153\) \(\Q(\sqrt{4705}) \) None \(8\) \(18\) \(18\) \(0\) \(-\) \(-\) \(-\) \(q+4q^{2}+9q^{3}+2^{4}q^{4}+(9-\beta )q^{5}+\cdots\)
294.6.a.w \(2\) \(47.153\) \(\Q(\sqrt{9601}) \) None \(8\) \(18\) \(53\) \(0\) \(-\) \(-\) \(-\) \(q+4q^{2}+9q^{3}+2^{4}q^{4}+(3^{3}-\beta )q^{5}+\cdots\)

Decomposition of \(S_{6}^{\mathrm{old}}(\Gamma_0(294))\) into lower level spaces

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