Properties

Label 315.3.ca
Level 315
Weight 3
Character orbit ca
Rep. character \(\chi_{315}(37,\cdot)\)
Character field \(\Q(\zeta_{12})\)
Dimension 152
Newform subspaces 3
Sturm bound 144
Trace bound 5

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Defining parameters

Level: \( N \) \(=\) \( 315 = 3^{2} \cdot 5 \cdot 7 \)
Weight: \( k \) \(=\) \( 3 \)
Character orbit: \([\chi]\) \(=\) 315.ca (of order \(12\) and degree \(4\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 35 \)
Character field: \(\Q(\zeta_{12})\)
Newform subspaces: \( 3 \)
Sturm bound: \(144\)
Trace bound: \(5\)
Distinguishing \(T_p\): \(2\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{3}(315, [\chi])\).

Total New Old
Modular forms 416 168 248
Cusp forms 352 152 200
Eisenstein series 64 16 48

Trace form

\( 152q + 2q^{2} + 10q^{7} + 12q^{8} + O(q^{10}) \) \( 152q + 2q^{2} + 10q^{7} + 12q^{8} - 18q^{10} + 8q^{11} - 8q^{13} + 276q^{16} - 8q^{17} + 72q^{20} - 88q^{22} + 14q^{23} + 48q^{25} + 148q^{26} + 26q^{28} - 104q^{31} - 82q^{32} + 164q^{35} - 84q^{37} + 52q^{38} - 118q^{40} - 144q^{41} - 180q^{43} - 148q^{46} - 204q^{47} - 508q^{50} + 272q^{52} + 112q^{53} - 240q^{55} + 444q^{56} - 274q^{58} - 124q^{61} + 736q^{62} - 152q^{65} + 134q^{67} + 160q^{68} - 592q^{70} + 8q^{71} - 252q^{73} + 688q^{76} - 372q^{77} - 584q^{80} + 294q^{82} - 948q^{83} + 608q^{85} - 688q^{86} - 336q^{88} - 760q^{91} + 332q^{92} - 172q^{95} - 520q^{97} - 754q^{98} + O(q^{100}) \)

Decomposition of \(S_{3}^{\mathrm{new}}(315, [\chi])\) into newform subspaces

Label Dim. \(A\) Field CM Traces $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\)
315.3.ca.a \(24\) \(8.583\) None \(2\) \(0\) \(4\) \(-6\)
315.3.ca.b \(64\) \(8.583\) None \(0\) \(0\) \(-4\) \(-4\)
315.3.ca.c \(64\) \(8.583\) None \(0\) \(0\) \(0\) \(20\)

Decomposition of \(S_{3}^{\mathrm{old}}(315, [\chi])\) into lower level spaces

\( S_{3}^{\mathrm{old}}(315, [\chi]) \cong \) \(S_{3}^{\mathrm{new}}(35, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(105, [\chi])\)\(^{\oplus 2}\)

Hecke characteristic polynomials

There are no characteristic polynomials of Hecke operators in the database