Properties

Label 1014.2.b
Level $1014$
Weight $2$
Character orbit 1014.b
Rep. character $\chi_{1014}(337,\cdot)$
Character field $\Q$
Dimension $26$
Newform subspaces $7$
Sturm bound $364$
Trace bound $10$

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Defining parameters

Level: \( N \) \(=\) \( 1014 = 2 \cdot 3 \cdot 13^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1014.b (of order \(2\) and degree \(1\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 13 \)
Character field: \(\Q\)
Newform subspaces: \( 7 \)
Sturm bound: \(364\)
Trace bound: \(10\)
Distinguishing \(T_p\): \(5\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(1014, [\chi])\).

Total New Old
Modular forms 210 26 184
Cusp forms 154 26 128
Eisenstein series 56 0 56

Trace form

\( 26 q - 2 q^{3} - 26 q^{4} + 26 q^{9} + O(q^{10}) \) \( 26 q - 2 q^{3} - 26 q^{4} + 26 q^{9} + 4 q^{10} + 2 q^{12} + 26 q^{16} + 4 q^{22} - 16 q^{23} - 38 q^{25} - 2 q^{27} + 32 q^{29} + 4 q^{30} - 26 q^{36} - 16 q^{38} - 4 q^{40} - 4 q^{42} - 16 q^{43} - 2 q^{48} - 46 q^{49} - 4 q^{51} + 24 q^{53} + 8 q^{55} + 8 q^{61} + 16 q^{62} - 26 q^{64} - 16 q^{69} + 16 q^{74} - 2 q^{75} - 8 q^{77} + 20 q^{79} + 26 q^{81} + 16 q^{82} + 24 q^{87} - 4 q^{88} + 4 q^{90} + 16 q^{92} - 16 q^{94} - 40 q^{95} + O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(1014, [\chi])\) into newform subspaces

Label Dim. \(A\) Field CM Traces $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
1014.2.b.a $2$ $8.097$ \(\Q(\sqrt{-1}) \) None \(0\) \(-2\) \(0\) \(0\) \(q+iq^{2}-q^{3}-q^{4}+iq^{5}-iq^{6}-2iq^{7}+\cdots\)
1014.2.b.b $2$ $8.097$ \(\Q(\sqrt{-1}) \) None \(0\) \(-2\) \(0\) \(0\) \(q-iq^{2}-q^{3}-q^{4}+2iq^{5}+iq^{6}+\cdots\)
1014.2.b.c $2$ $8.097$ \(\Q(\sqrt{-1}) \) None \(0\) \(2\) \(0\) \(0\) \(q-iq^{2}+q^{3}-q^{4}+3iq^{5}-iq^{6}+\cdots\)
1014.2.b.d $4$ $8.097$ \(\Q(\zeta_{12})\) None \(0\) \(-4\) \(0\) \(0\) \(q+\zeta_{12}q^{2}-q^{3}-q^{4}-\zeta_{12}^{2}q^{5}-\zeta_{12}q^{6}+\cdots\)
1014.2.b.e $4$ $8.097$ \(\Q(\zeta_{12})\) None \(0\) \(4\) \(0\) \(0\) \(q+\zeta_{12}q^{2}+q^{3}-q^{4}+(2\zeta_{12}+\zeta_{12}^{2}+\cdots)q^{5}+\cdots\)
1014.2.b.f $6$ $8.097$ 6.0.153664.1 None \(0\) \(-6\) \(0\) \(0\) \(q-\beta _{5}q^{2}-q^{3}-q^{4}+(-2\beta _{1}-\beta _{3}+\cdots)q^{5}+\cdots\)
1014.2.b.g $6$ $8.097$ 6.0.153664.1 None \(0\) \(6\) \(0\) \(0\) \(q+\beta _{5}q^{2}+q^{3}-q^{4}+(\beta _{1}+\beta _{3}-\beta _{5})q^{5}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(1014, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(1014, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(26, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(39, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(78, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(169, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(338, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(507, [\chi])\)\(^{\oplus 2}\)