Properties

Label 2668.2.a
Level $2668$
Weight $2$
Character orbit 2668.a
Rep. character $\chi_{2668}(1,\cdot)$
Character field $\Q$
Dimension $50$
Newform subspaces $5$
Sturm bound $720$
Trace bound $1$

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Defining parameters

Level: \( N \) \(=\) \( 2668 = 2^{2} \cdot 23 \cdot 29 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 2668.a (trivial)
Character field: \(\Q\)
Newform subspaces: \( 5 \)
Sturm bound: \(720\)
Trace bound: \(1\)
Distinguishing \(T_p\): \(3\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_0(2668))\).

Total New Old
Modular forms 366 50 316
Cusp forms 355 50 305
Eisenstein series 11 0 11

The following table gives the dimensions of the cuspidal new subspaces with specified eigenvalues for the Atkin-Lehner operators and the Fricke involution.

\(2\)\(23\)\(29\)FrickeDim.
\(-\)\(+\)\(+\)\(-\)\(12\)
\(-\)\(+\)\(-\)\(+\)\(13\)
\(-\)\(-\)\(+\)\(+\)\(10\)
\(-\)\(-\)\(-\)\(-\)\(15\)
Plus space\(+\)\(23\)
Minus space\(-\)\(27\)

Trace form

\( 50q + 4q^{3} - 4q^{7} + 50q^{9} + O(q^{10}) \) \( 50q + 4q^{3} - 4q^{7} + 50q^{9} + 4q^{11} - 4q^{13} + 4q^{17} - 8q^{21} + 42q^{25} + 40q^{27} + 6q^{29} + 4q^{35} - 12q^{37} - 36q^{39} + 16q^{41} + 8q^{43} + 24q^{45} + 4q^{47} + 30q^{49} + 56q^{51} - 36q^{53} - 4q^{55} + 32q^{57} + 20q^{59} - 28q^{61} - 32q^{63} - 16q^{65} - 24q^{67} + 8q^{69} + 4q^{71} + 8q^{73} + 32q^{75} + 36q^{77} + 8q^{79} + 82q^{81} - 32q^{83} - 4q^{85} - 8q^{89} - 16q^{91} + 20q^{93} - 16q^{95} - 24q^{97} + 44q^{99} + O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(2668))\) into newform subspaces

Label Dim. \(A\) Field CM Traces A-L signs $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\) 2 23 29
2668.2.a.a \(1\) \(21.304\) \(\Q\) None \(0\) \(-2\) \(2\) \(0\) \(-\) \(-\) \(-\) \(q-2q^{3}+2q^{5}+q^{9}-2q^{13}-4q^{15}+\cdots\)
2668.2.a.b \(10\) \(21.304\) \(\mathbb{Q}[x]/(x^{10} - \cdots)\) None \(0\) \(-3\) \(0\) \(-5\) \(-\) \(-\) \(+\) \(q-\beta _{1}q^{3}+(\beta _{5}+\beta _{7}-\beta _{8})q^{5}+(-\beta _{5}+\cdots)q^{7}+\cdots\)
2668.2.a.c \(12\) \(21.304\) \(\mathbb{Q}[x]/(x^{12} - \cdots)\) None \(0\) \(5\) \(0\) \(3\) \(-\) \(+\) \(+\) \(q+\beta _{1}q^{3}+\beta _{4}q^{5}+\beta _{8}q^{7}+(1+\beta _{1}+\cdots)q^{9}+\cdots\)
2668.2.a.d \(13\) \(21.304\) \(\mathbb{Q}[x]/(x^{13} - \cdots)\) None \(0\) \(-7\) \(0\) \(-5\) \(-\) \(+\) \(-\) \(q+(-1+\beta _{1})q^{3}-\beta _{4}q^{5}-\beta _{7}q^{7}+(1+\cdots)q^{9}+\cdots\)
2668.2.a.e \(14\) \(21.304\) \(\mathbb{Q}[x]/(x^{14} - \cdots)\) None \(0\) \(11\) \(-2\) \(3\) \(-\) \(-\) \(-\) \(q+(1-\beta _{1})q^{3}+\beta _{8}q^{5}-\beta _{5}q^{7}+(2-\beta _{1}+\cdots)q^{9}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_0(2668))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_0(2668)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_0(23))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(29))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(46))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(58))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(92))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(116))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(667))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(1334))\)\(^{\oplus 2}\)