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Properties

Label 2299.1.m
Level $2299$
Weight $1$
Character orbit 2299.m
Rep. character $\chi_{2299}(493,\cdot)$
Character field $\Q(\zeta_{10})$
Dimension $12$
Newform subspaces $3$
Sturm bound $220$
Trace bound $7$

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Defining parameters

Level: \( N \) \(=\) \( 2299 = 11^{2} \cdot 19 \)
Weight: \( k \) \(=\) \( 1 \)
Character orbit: \([\chi]\) \(=\) 2299.m (of order \(10\) and degree \(4\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 209 \)
Character field: \(\Q(\zeta_{10})\)
Newform subspaces: \( 3 \)
Sturm bound: \(220\)
Trace bound: \(7\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{1}(2299, [\chi])\).

Total New Old
Modular forms 68 44 24
Cusp forms 20 12 8
Eisenstein series 48 32 16

The following table gives the dimensions of subspaces with specified projective image type.

\(D_n\) \(A_4\) \(S_4\) \(A_5\)
Dimension 12 0 0 0

Trace form

\( 12 q - 3 q^{4} + 4 q^{5} - 3 q^{7} - 3 q^{9} + O(q^{10}) \) \( 12 q - 3 q^{4} + 4 q^{5} - 3 q^{7} - 3 q^{9} - 3 q^{16} - 3 q^{17} + q^{19} + 4 q^{20} - 6 q^{23} + q^{25} + 2 q^{28} - q^{35} - 3 q^{36} + 2 q^{43} - 6 q^{45} + 4 q^{47} - 4 q^{49} - 3 q^{61} - 3 q^{63} - 3 q^{64} - 3 q^{68} + 2 q^{73} - 4 q^{76} - q^{80} - 3 q^{81} + 2 q^{83} - q^{85} + 4 q^{92} - 3 q^{95} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{1}^{\mathrm{new}}(2299, [\chi])\) into newform subspaces

Label Char Prim Dim $A$ Field Image CM RM Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
2299.1.m.a 2299.m 209.m $4$ $1.147$ \(\Q(\zeta_{10})\) $D_{5}$ \(\Q(\sqrt{-19}) \) None \(0\) \(0\) \(-2\) \(-3\) \(q+\zeta_{10}^{4}q^{4}+(\zeta_{10}^{2}+\zeta_{10}^{4})q^{5}+(-1+\cdots)q^{7}+\cdots\)
2299.1.m.b 2299.m 209.m $4$ $1.147$ \(\Q(\zeta_{10})\) $D_{5}$ \(\Q(\sqrt{-19}) \) None \(0\) \(0\) \(3\) \(-2\) \(q+\zeta_{10}^{4}q^{4}+(1-\zeta_{10})q^{5}+(-\zeta_{10}+\cdots)q^{7}+\cdots\)
2299.1.m.c 2299.m 209.m $4$ $1.147$ \(\Q(\zeta_{10})\) $D_{5}$ \(\Q(\sqrt{-19}) \) None \(0\) \(0\) \(3\) \(2\) \(q+\zeta_{10}^{4}q^{4}+(1-\zeta_{10})q^{5}+(\zeta_{10}-\zeta_{10}^{2}+\cdots)q^{7}+\cdots\)

Decomposition of \(S_{1}^{\mathrm{old}}(2299, [\chi])\) into lower level spaces

\( S_{1}^{\mathrm{old}}(2299, [\chi]) \simeq \) \(S_{1}^{\mathrm{new}}(209, [\chi])\)\(^{\oplus 2}\)